Image Graphcenter.svg thumb right A graph with central points colored red. These are the three vertices A such that d A , B 3 for all vertices B . Each black vertex is a distance of at least 4 from some other vertex. The center or Camille Jordan Jordan center ref name WF Wasserman, Stanley, and Faust, Katherine 1994 , Social Network Analysis Methods and Applications , page 185. Cambridge Cambridge University Press. ISBN 0521382696 ref of a Graph mathematics graph is the set of all vertices of minimum Eccentricity graph theory eccentricity , ref McHugh, James A., http www.cs.njit.edu mchugh psswrd web course materials graph theory alg graph theory text html chap 1 text v3.html Algorithmic Graph Theory ref that is, the set of all vertices A where the greatest distance d A , B to other vertices B is minimal. Equivalently, it is the set of vertices with eccentricity equal to the graph s radius graph theory radius . ref MathWorld urlname GraphCenter title Graphcenter ref Thus vertices in the center central points minimize the maximal distance from other points in the graph. Finding the center of a graph is useful in facility location problem s where the goal is to minimize the worst case distance to the facility. For example, placing a hospital at a central point reduces the longest distance the ambulance has to travel. The concept of the center of a graph is related to the centrality Closeness centrality closeness centrality measure in social network analysis , which is the reciprocal of the mean of the distances d A , B . ref name WF References references Category Graph theory objects ... more details
Selfref For information about graphs on Wikipedia, see Wikipedia Graphs and charts . Wiktionary Graph may refer to A Information graphics graphic such as a line chart , Plot graphics plot , chart or diagram depicting the relationship between two or more variables used, for instance, in visualising scientific data. In mathematics Graph mathematics , is a set of vertices and edges. Graph theory Graph of a function In computer science Graph data structure , an abstract data type representing relationships or connections Graph software , the name of a software application for mathematical plotting Conceptual graph , a model for knowledge representation and reasoning Other uses HMS Graph P715 , a submarine of the Royal Navy United Kingdom See also Grapheme linguistics Graphemics wiktionary graphy graphy suffix Latin for to write or draw Graf Graff disambiguation List of information graphics software Disambiguation de Graph es Grafo desambiguaci n eu Grafo argipena fr Graphe hu Gr f egy rtelm s t lap ms Graf ja ru uk ur Graph ... more details
Orphan date November 2006 Image s graph.gif right thumb 275px Visual representation of an S graph to efficiently solving batch process scheduling problems in chemical plant s. ref Cite journal last Holczinger first T. coauthors J Romero, L Puigjaner, F Friedler title Scheduling of Multipurpose Batch Processes with Multiple Batches of the Products volume 30 pages 305 312 date 2002 12 02 unused data Hungarian Journal for Industrial Chemistry ref ref name AICE Cite journal last Romero first Javier coauthors Luis Puigjaner, Tibor Holczinger, Ferenc Friedler title Scheduling intermediate storage multipurpose batch plants using the S graph journal American Institute of Chemical Engineers volume 50 issue 2 pages 403 417 date 2004 02 18 ref S graph is especially developed for the problems with non intermediate storage NIS policy, which often appears in chemical productions, but it is also capable to solve problems with unlimited intermediate storage UIS policy. ref name AICE Overview S graph representation has the advantage of exploiting problem specific knowledge to develop efficient scheduling algorithm s. ref name AICE There are products, and a set of task, which have to be performed to produce a product. There are dependencies between the tasks, and every task has a set of equipments, that can perform the task. Different processing times can be set for the same task in different equipments. It is also possible to have more equipment units from the same type, or define changeover times between two task in one equipment. There are two types of the scheduling problems The number of batches to produce is set, and we try to minimize the makespan processing time . Every product has a revenue, and a time horizon is set. The objective is to maximize the revenue in this fixed time horizon. S graph framework also contains Combinatorics combinatoric algorithm s to solve both of these problems. References Reflist External links http www.s graph.com S graph website Category Job scheduling ... more details
infobox graph image File E7 graph.svg 241px image caption Gosset graph 3 sub 21 sub BR Two vertices coincide in the center of this graph. Edges also coincide with this projection. name Gosset graph namesake Thorold Gosset vertices 56 edges 756 automorphisms 2903040 diameter 3 radius 3 girth 3 properties Distance regular graph br Integral graph Integral br Vertex transitive graph Vertex transitive The Gosset graph , named after Thorold Gosset , is a specific regular graph 1 n skeleton skeleton of the 7 dimensional Gosset 3 21 polytope 3 sub 21 sub polytope with 56 vertices and valency 27. Construction The Gosset graph can be explicitly constructed as follows the 56 vertices are the vectors in R sup 8 sup , obtained by permuting the coordinates and possibly taking the opposite of the vector 3, 3, &minus 1, &minus 1, &minus 1, &minus 1, &minus 1, &minus 1 . Two such vectors are adjacent when their inner product is 8. Properties In the above representation, two vertices are at distance two when their inner product is &minus 8 and at distance three when their inner product is &minus 24 which is only possible if the vectors are each other s opposite . The Gosset graph is Distance regular graph distance regular with diameter three. The Graph automorphism automorphism group of the Gosset graph is isomorphic to the Coxeter group E7 mathematics E sub 7 sub and hence has order 2903040. The Gosset 3 sub 21 sub polytope is a semiregular polytope . Therefore the automorphism group of the Gosset graph, E sub 7 sub , Group action acts transitively upon its vertices, making it a vertex transitive graph . The characteristic polynomial of the Gosset graph is math x 27 x 9 7 x 1 27 x 3 21 . , math Therefore this graph is an integral graph . References MathWorld title Gosset Graph urlname GossetGraph Category Individual graphs Category Regular graphs combin stub fr Graphe de Gosset ... more details
In the mathematical discipline of graph theory , a biconnected graph is a connected graph mathematics graph with no Articulation vertex articulation vertices . In other words, a biconnected graph is connected and nonseparable , meaning that if any vertex graph theory vertex were to be removed, the graph will remain connected. The property of being K vertex connected graph 2 connected is equivalent to biconnectivity, with the caveat that the complete graph of two vertices is sometimes regarded as biconnected but not 2 connected. This property is especially useful in maintaining a graph with a two fold Redundancy engineering redundancy , to prevent disconnection upon the removal of a single edge graph theory edge or connection . The use of biconnected graphs is very important in the field of networking see Network flow , because of this property of redundancy. Definition A biconnected undirected graph is a connected graph that is not broken into disconnected pieces by deleting any single vertex and its incident edges . A biconnected directed graph is one such that for any two vertices v and w there are two directed paths from v to w which have no vertices in common other than v and w . class wikitable style text align center Nonseparable or 2 connected graphs or blocks with n nodes OEIS id A002218 Vertices Number of Possibilities 1 0 2 1 3 1 4 3 5 10 6 56 7 468 8 7123 9 194066 10 9743542 11 900969091 12 153620333545 13 48432939150704 14 28361824488394169 15 30995890806033380784 16 63501635429109597504951 17 244852079292073376010411280 18 1783160594069429925952824734641 19 24603887051350945867492816663958981 Examples http mathworld.wolfram.com images eps gif BiconnectedGraphs 1000.gif See also Biconnected component References Eric W. Weisstein. Biconnected Graph. From MathWorld ... graph , in Dictionary of Algorithms and Data Structures online , Paul E. Black, ed., U.S. National ... dads HTML biconnectedGraph.html Category Graph families Category Graph connectivity fa ... more details
In mathematics , a convex graph may be a convex bipartite graph a convex plane graph the graph of a function graph of a convex function disambig ... more details
about sets of vertices connected by edges graphs of mathematical functions Graph of a function statistical graphs Chart further Graph theory Image 6n graf.svg thumb 250px A graph drawing drawing of a labeled graph on 6 vertices and 7 edges. In mathematics , a graph is an abstract representation of a set ... by mathematical abstractions called Vertex graph theory vertices , and the links that connect some pairs of vertices are called edges . Typically, a graph is depicted in diagrammatic form ... graph symmetric . For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this is an undirected graph, because if person A shook ... B, then this graph is directed, because knowledge of someone is not necessarily a symmetric ... type of graph is called a directed graph and the edges are called directed edges or arcs ... subject studied by graph theory . The word graph was first used in this sense by James Joseph Sylvester J.J. Sylvester in 1878. ref Cite book title Handbook of graph theory first1 Jonathan L. last1 Gross ... http books.google.com ?id mKkIGIea BkC postscript None ref Definitions Definitions in graph theory .... Graph Image Multigraph.svg thumb 125px A general example of a graph actually, a pseudograph ... and Kawada, 69 J , p. 234 or Biggs, p. 4. ref a graph is an ordered pair G V , ..., this type of graph may be described precisely as graph mathematics Undirected graph undirected and graph mathematics Simple graph simple . Other senses of graph stem from different conceptions of the edge ... of the edge. A vertex may exist in a graph and not belong to an edge. V and E are usually taken ... graphs because many of the arguments fail in the infinite graph infinite case . The order of a graph is math V math the number of vertices . A graph s size is math E math , the number of edges. The degree ... at both ends a loop graph theory loop is counted twice. For an edge u , v , graph theorists ... more details
Graph equations are equations in which the unknowns are Graph theory graphs . One of the central questions of graph theory concerns the notion of Graph isomorphism isomorphism . We ask When are two graphs the same i.e, graph isomorphism ? The graphs in question may be expressed differently in terms of graph equations. ref http www3.interscience.wiley.com journal 113386917 abstract?CRETRY 1&SRETRY 0 Bibliography on Graph equations ref What are the graphs root of a function solutions G and H such that the line graph of G is same as the total graph of H ? What are G and H such that L G T H ? . For example, G K sub 3 sub , and H K sub 2 sub are the solutions of the graph equation L K sub 3 sub T K sub 2 sub and G K sub 4 sub , and H K sub 3 sub are the solutions of the graph equation L K sub 4 sub T K sub 3 sub . gallery Image Complete graph K2.svg math K 2 math Image Complete graph K3.svg math K 3 math Image Complete graph K4.svg math K 4 math gallery center Note that T K sub 3 sub is a 4 regular graph on 6 vertices. Selected publications Graph equations for line graphs and total graphs, DM Cvetkovic, SK Simic &ndash Discrete Mathematics journal Discrete Mathematics , 1975 Graph equations, graph inequalities and a fixed point theorem, DM Cvetkovic, IB Lackovic, SK Simic &ndash Publ. Inst. Math. Belgrade ., 1976 &ndash elib.mi.sanu.ac.yu , PUBLICATIONS DE L INSTITUT MATH MATIQUE Nouvelle s rie, tome 20 34 , 1976, Graphs whose complement and line graph are isomorphic, M Aigner &ndash Journal of Combinatorial Theory , 1969 Solutions of some further graph equations, Bhat Nayak Vasanti N. Vasanti N. Bhat Nayak , Ranjan N. Naik &ndash Discrete Mathematics journal Discrete Mathematics , 47 1983 169&ndash 175 More Results on the Graph Equation G2 G, M Capobianco, SR Kim &ndash Graph Theory, Combinatorics, and Algorithms Proceedings of , 1995 &ndash Wiley Interscience Graph equation ... Graph Equation Category Graph theory ... more details
east.svg frameless center 40px File Shrikhande graph square.svg center 120px Shrikhande graph link Shrikhande graph File Arrow west.svg frameless center 40px File Paley13 no label.svg center 120px Paley ... regular Strongly regular graph strongly regular File Arrow south.svg frameless center 15px File F26A graph.svg center 120px F26A graph link F26A graph File Arrow west.svg frameless center 40px File Nauru graph.svg center 120px Nauru graph link Nauru graph Symmetric graph symmetric arc transitive Symmetric graph t transitive, t 2 File Arrow south.svg frameless center 15px if connected File Holt graph.svg center 120px Holt graph link Holt graph File Arrow east.svg frameless center 40px File Folkman Lombardi.svg center 120px Folkman graph link Folkman graph File Arrow east.svg frameless center 40px File Biclique K 3 5.svg center 120px Complete bipartite graph K3,5 link Complete bipartite ... Edge transitive graph edge transitive File Arrow south.svg frameless center 15px File Arrow south.svg ... graph.neato.svg center 120px Frucht graph link Frucht graph Vertex transitive graph vertex transitive Regular graph regular File Arrow north.svg frameless center 15px Image Z 2xZ 3.svg center 120px ...In the mathematics mathematical field of graph theory , an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving the edge vertex connectivity. Formally, an automorphism of a graph G V , E is a permutation of the vertex set V , such that the pair of vertices u , v form an edge if and only if the pair u , v also form an edge. That is, it is a graph ... graph s and for undirected graph s. The Function composition composition of two automorphisms is another automorphism, and the set of automorphisms of a given graph, under the composition operation, forms a Group mathematics group , the automorphism group of the graph. In the opposite direction, by Frucht s theorem , all groups can be represented as the automorphism group of a connected graph ... more details
, their center of perspectivity, and their axis of perspectivity. The Desargues graph has one ...Infobox graph name Desargues graph image Image DesarguesGraph.svg 220px namesake G rard Desargues vertices ... 6 radius 5 diameter 5 properties Cubic graph Cubic br Distance regular graph Distance regular br hamiltonian graph Hamiltonian br Bipartite graph Bipartite br Symmetric graph Symmetric In the mathematics mathematical field of graph theory , the Desargues graph is a Distance transitive graph distance transitive cubic graph with 20 vertices and 30 edges. ref MathWorld urlname DesarguesGraph title Desargues Graph ref It is named after G rard Desargues , arises from several different combinatorial constructions, has a high level of symmetry, is the only known planar graph non planar cubic partial cube , and has been applied in chemical databases. The name Desargues graph has also been used to refer to the complement of the Petersen graph . ref citation last Kagno first I. N. title Desargues ... Constructions There are several different ways of constructing the Desargues graph It is the generalized Petersen graph G 10, 3 . To form the Desargues graph in this way, connect ten of the vertices ... pairs of vertices at distance three in a second decagon. The Desargue graph consists of the 20 ... points of the other. It is the Levi graph of the Desargues configuration . This configuration ... of points and lines forming this configuration, and the configuration and the graph take their name from it. It is the bipartite double cover of the Petersen graph , formed by replacing each Petersen graph vertex by a pair of vertices and each Petersen graph edge by a pair of crossed edges. It is the Kneser graph bipartite Kneser graph H sub 5,2 sub . Its vertices can be labeled by the ten two element ... vertices when one of the corresponding sets is a subset of the other. The Desargues graph is Hamiltonian graph Hamiltonian and can be constructed from the LCF notation 5, 5,9, 9 sup 5 sup Algebraic properties ... more details
infobox graph name Windmill graph image Image Windmill graph Wd 5,4 .svg 220px image caption The Windmill graph Wd 5,4 . vertices k 1 n 1 edges nk k 1 2 automorphisms girth 3 if k 2 diameter 2 radius 1 chromatic number k chromatic index n k 1 notation Wd k , n properties In the mathematics mathematical field of graph theory , the windmill graph Wd k , n is a simple graph simple undirected graph with k 1 n 1 vertices and nk k 1 2 edges. ref MathWorld urlname WindmillGraph title Windmill Graph ref It is defined for k 2 and n 2. The windmill graph Wd k , n can be constructed by joining n copies of the complete graph K sub k sub with a common vertex. ref Gallian, J. A. Dynamic Survey DS6 Graph Labeling. Electronic J. Combinatorics, DS6, 1 58, Jan. 3, 2007. http www.combinatorics.org Surveys ds6.pdf . ref It has girth 3 if k 2 , radius 1 and diameter 2. By removing the central vertex of the windmill graph, it can be proved that it is a 1 k vertex connected graph vertex connected graph . Each copy of the complete graph K sub k sub is k 1 k edge connected graph edge connected graph. Therefore, the windmill graph is k 1 edge connected. It is trivially perfect graph trivially perfect and a block graph . By construction, the windmill graph Wd 3, n is the friendship graph F sub n sub , the windmill graph Wd 2, n is the Star graph theory star graph S sub n sub and the windmill graph Wd 3,2 is the butterfly graph . Labeling and colouring The windmill graph has chromatic number k and chromatic index n k 1 . Its chromatic polynomial can be deduced form the chromatic polynomial of the complete graph and is equal to math prod i 0 k 1 x i n math The windmill graph Wd k , n is proved not Graceful labeling graceful if k 5. ref K. M. Koh, D. G. Rogers, H. K. Teo, and K. Y. Yap, Graceful graphs ... windmills, Graph Theory and Combinatorics, Pitman, London 1979 18 37. ref This is known to be true ... Windmill graphs.svg thumb 550px center Small windmill graphs. References reflist Category Parametric ... more details
Primal graph may refer to Primal graph hypergraphs of a hypergraph A primal graph may be the planar graph from which a dual graph is formed Primal constraint graph disambig ... more details
, such as the center vertex in the drawing, the remaining graph is Hamiltonian. In addition, this drawing ...Infobox graph name Petersen graph image Image Petersen1 tiny.svg 200px image caption The Petersen graph ... 3 chromatic index 4 fractional chromatic index 3 properties Cubic graph Cubic br Strongly regular graph Strongly regular br Distance transitive graph Distance transitive br Snark graph theory Snark In the mathematics mathematical field of graph theory , the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is named for Julius Petersen , who in 1898 constructed it to be the smallest Bridge graph theory bridgeless cubic graph with no three edge coloring. ref citation url http www.win.tue.nl aeb drg graphs Petersen.html title The Petersen graph first Andries E. last Brouwer authorlink Andries Brouwer ref Although the graph is generally credited to Petersen ... authorlink Alfred Kempe year 1886 txt . Donald Knuth states that the Petersen graph is a remarkable ... File Kneser graph KG 5,2 .svg thumb left Petersen graph as Kneser graph math KG 5,2 math The Petersen graph is the complement graph complement of the line graph of math K 5 math . It is also the Kneser graph math KG 5,2 math this means that it has one vertex for each 2 element subset of a 5 ... subsets are disjoint from each other. As a Kneser graph of the form math KG 2n 1,n 1 math it is an example of an odd graph . Geometrically, the Petersen graph is the graph formed by the vertices and edges ... together. Embeddings The Petersen graph is planar graph nonplanar . Any nonplanar graph has as minor graph theory minor s either the complete graph math K 5 math , or the complete bipartite graph math K 3,3 math , but the Petersen graph has both as minors. The math K 5 math minor can be formed .... Image Petersen graph, two crossings.svg thumb right The Petersen graph has Crossing number graph theory ... more details
Infobox graph name Bull graph image Image Bull graph.circo.svg 170px image caption The Bull graph namesake vertices 5 edges 5 automorphisms 2 Z 2 Z diameter 3 girth 3 radius 2 chromatic number 3 chromatic index 3 properties planar graph Planar br unit distance graph Unit distance In the mathematics mathematical field of graph theory , the bull graph is a planar graph planar undirected graph with 5 vertices and 5 edges, in the form of a triangle with two disjoint pendant edges. ref MathWorld urlname BullGraph title Bull Graph ref It has chromatic number 3, chromatic index 3, radius 2, diameter 3 and girth graph theory girth 3. It is also a 1 k vertex connected graph vertex connected graph and a 1 k edge connected graph edge connected graph . Bull free graphs A graph is bull free if it has no bull as an induced subgraph . The triangle free graph s are bull free graphs, since every bull contains a triangle. The perfect graph strong perfect graph theorem was proven for bull free graphs long before its proof for general graphs, ref citation last1 Chv tal first1 V. author1 link V clav Chv tal last2 Sbihi first2 N. title Bull free Berge graphs are perfect journal Graphs and Combinatorics volume 3 year 1987 pages 127 139 issue 1 doi 10.1007 BF01788536 . ref and a polynomial time recognition algorithm for Bull free perfect graphs is known. ref citation last1 Reed first1 B. last2 Sbihi first2 N. title Recognizing bull free perfect graphs journal Graphs and Combinatorics volume 11 year 1995 pages 171 178 issue 2 doi 10.1007 BF01929485 . ref Maria Chudnovsky and Shmuel Safra have studied bull free graphs more generally, showing that any such graph must have either a large clique graph ... thumb left 200px center The three graphs with a chromatic polynomial equal to math x 2 x 1 3x math . center The chromatic polynomial of the bull graph is math x 2 x 1 3x math . Two other graphs are chromatically equivalent to the bull graph. Its characteristic polynomial is math x x 2 x 3 x 2 ... more details
infobox graph name Friendship graph image Image Friendship graph 8.svg 120px image caption The friendship graph F sub 8 sub . vertices 2n 1 edges 3n automorphisms chromatic number 3 girth 3 diameter 2 radius 1 chromatic index 2n notation F sub n sub properties Unit distance graph Unit distance br planar graph Planar br Eulerian graph Eulerian br Factor critical graph factor critical In the mathematics mathematical field of graph theory , the friendship graph or dutch windmill graph or n fan F sub n sub is a planar graph planar undirected graph with 2n 1 vertices and 3n edges. ref MathWorld urlname DutchWindmillGraph title Dutch Windmill Graph ref The friendship graph F sub n sub can be constructed by joining n copies of the cycle graph C sub 3 sub with a common vertex. ref Gallian, J. A. Dynamic Survey DS6 Graph Labeling. Electronic J. Combinatorics, DS6, 1 58, Jan. 3, 2007. http www.combinatorics.org Surveys ds6.pdf . ref By construction, the friendship graph F sub n sub is isomorphic to the windmill graph Wd 3, n . It is Unit distance graph unit distance with girth 3, diameter 2 and radius 1. The graph F sub 2 sub is isomorphic to the butterfly graph . Friendship theorem The friendship ... of graph theory journal Studia Sci. Math. Hungar. volume 1 year 1966 pages 215 235 . ref ... The friendship graph has chromatic number 3 and chromatic index 2n . Its chromatic polynomial can be deduced from the chromatic polynomial of the cycle graph C sub 3 sub and is equal to math x 2 n x 1 n x math . The friendship graph F sub n sub is Edge graceful labeling edge graceful if and only ... graph is Factor critical graph factor critical . Extremal graph theory According to extremal graph theory , every graph with sufficiently many edges relative to its number of vertices must contain a k fan. More specifically, this is true for an n vertex graph if the number of edges is math left ... on the number of edges in a triangle free graph , and they are the best possible bounds for this problem ... more details
of graphs . Example The two graphs shown below are isomorphic, despite their different looking graph drawing drawings . class wikitable style margin 1em auto 1em auto Graph G Graph H An isomorphism br between G and H style padding left 2em padding right 2em Image Graph isomorphism a.svg 100px style padding left 1em padding right 1em Image Graph isomorphism b.svg 210px align center style background ...In graph theory , an isomorphism of graph mathematics graph s G and H is a bijection between the vertex ... bijection. In the above definition, graphs are understood to be directed graph undirected labeled graph non labeled weighted graph non weighted graphs. However, the notion of isomorphism may be applied to all other variants of the notion of graph, by adding the requirements to preserve the corresponding ... exception. When spoken about graph labeling with unique labels , commonly taken from the integer range 1,..., n , where n is the number of the vertices of the graph, two labeled graphs are said to be isomorphic ... when the bijection is a mapping of a graph onto itself, i.e., when G and H are one and the same graph, the bijection is called an graph automorphism automorphism of G . The graph isomorphism is an equivalence ... , e.g., of graph isomorphism , captures the informal notion that some objects have the same structure ... digraph s, labeled graph s, colored graph s, rooted tree s and so on. The isomorphism relation ... the elements of structure which define the object type in question arc graph theory arc s, labels, vertex edge colors, the root of the rooted tree, etc. The notion of graph isomorphism allows us to distinguish graph properties inherent to the structures of graphs themselves from properties associated with graph representations graph drawing s, graph data structure data structures for graphs , graph labeling s, etc. For example, if a graph has exactly one cycle graph theory cycle , then all graphs ... the vertices of a graph are represented by the integer s 1, 2,... N , then the expression math sum ... more details
BR The 7 cycles of the wheel graph W sub 4 sub . For odd values of n , W sub n sub is a perfect graph with chromatic number 3 the vertices of the cycle can be given two colors, and the center vertex ... BF01864150 pages 23 30 . ref The chromatic polynomial of the wheel graph W sub n sub is center math P W n x x x 2 n 1 1 n x 2 . math center In matroid theory, two particularly important special classes ...infobox graph name Wheel graph image Image Wheel graphs.svg 220px image caption Several examples of wheel ... cup 1 pm sqrt 1 n math properties Hamiltonian graph Hamiltonian br Dual graph Self dual br Planar graph Planar notation W sub n sub In the mathematical discipline of graph theory , a wheel graph W sub n sub is a graph with n vertices, formed by connecting a single vertex to all vertices of an n 1 Cycle graph cycle . The numerical notation for wheels is used inconsistently in the literature some authors instead use n to refer to the length of the cycle, so that their W sub n sub is the graph we denote W sub n 1 sub . ref mathworld urlname WheelGraph title Wheel Graph ref A wheel graph can also ... are planar graph s, and as such have a unique planar embedding. More specifically, every wheel graph is a Halin graph . They are self dual the Dual graph planar dual of any wheel graph is an isomorphic graph. Any maximal planar graph, other than K sub 4 sub W sub 4 sub , contains as a subgraph either W sub 5 sub or W sub 6 sub . There is always a Hamiltonian cycle in the wheel graph and there are math .... W sub 7 sub is the only wheel graph that is a unit distance graph in the Euclidean plane. ref citation ... theory he had conjectured that the complete graph has the smallest Ramsey number among all graphs ... 17 while the complete graph with the same chromatic number, K sub 4 sub , has Ramsey number 18. ref ... 31 . ref That is, for every 17 vertex graph G , either G or its complement contains W sub 6 sub as a subgraph, while neither the 17 vertex Paley graph nor its complement contains a copy of K sub 4 sub ... more details
wiktionarypar Periodic Graph Periodic graph periodic graph Periodic graphs periodic graphs Periodic graph can mean Periodic graph crystallography or crystal net , a Euclidean graph representing the atomic or molecular structure of a crystal. Periodic graph geometry , a Euclidean graph preserved under a lattice of translations. Periodic graphgraph theory , a graph that is periodic with respect to a graph theoretic operator disambig ... more details
An acyclic graph may refer to Directed acyclic graph , a directed graph without any directed cycles Forest graph theory , an undirected acyclic graph Polytree , a directed graph without any undirected cycles mathdab ... more details
Distinguish Factor graph Cleanup date January 2010 Image Desargues graph 3color edge.svg thumb 200px 1 factorization of Desargues graph each color class is a 1 factor. Image Petersen graph factors.svg right thumb 200px Petersen graph can be partitioned into a 1 factor red and a 2 factor blue . However, the graph is not 1 factorable. In graph theory , a factor of a graph G is a spanning subgraph , i.e., a subgraph that has the same vertex set as G . A k factor of a graph is a spanning k Regular graph regular subgraph, and a k factorization partitions the edges of the graph into disjoint k factors. A graph G is said to be k factorable if it admits a k factorization. In particular, a 1 factor is a perfect matching , and a 1 factorization of a k regular graph is an edge coloring with k colors. A 2 factor is a collection of Cycle graph theory cycles that spans all vertices of the graph. 1 factorization If a graph is 1 factorable, then it has to be a regular graph . However, not all regular graphs are 1 factorable. A k regular graph is 1 factorable if it has chromatic index k examples of such graphs include Any regular bipartite graph . ref harvtxt Harary 1969 , Theorem 9.2, p. 85. harvtxt ... bipartite graph contains a perfect matching. One can then remove the perfect matching to obtain a k &minus 1 regular bipartite graph, and apply the same reasoning repeatedly. Any complete graph with an even number of nodes see Complete graphs below . ref harvtxt Harary 1969 , Theorem ... 1, and these graphs are not 1 factorable examples of such graphs include Any regular graph with an odd number of nodes. Petersen graph . Complete graphs File Complete edge coloring.svg thumb 200px An easy ... again with the eight vertices as described and join the center point to the point in the circle directly ... can also be looked at as a 1 factor of the complete graph on eight vertices, K sub 8 sub . Continuing ... a 1 factorization of K sub 2 n sub for all n . A 1 factorization of a complete graph corresponds ... more details
In mathematics, a k ultrahomogeneous graph is a graph mathematics graph in which every graph isomorphism isomorphism between two of its induced subgraph s of at most k vertices can be extended to an graph automorphism automorphism of the whole graph. If a graph is 5 ultrahomogeneous, then it is ultrahomogeneous for every k . The only finite connected graphs of this type are complete graph s, Tur n graph s, 3 × 3 rook s graph s, and the 5 cycle graph cycle . There are only two connected graphs that are 4 ultrahomogeneous but not 5 ultrahomogeneous the Schl fli graph and its complement. The proof relies on the classification of finite simple groups . ref harvtxt Buczak 1980 harvtxt Cameron 1980 harvtxt Devillers 2002 . ref The infinite Rado graph is countably ultrahomogeneous. Notes reflist Category Graph theory ... more details
Citations missing date October 2008 In the mathematics mathematical field of graph theory , a quartic graph is a graph mathematics graph where all vertex graph theory vertices have degree graph theory degree 4. In other words a quartic graph is a 4 regular graph . A biquartic graph is a quartic bipartite graph . It is an open conjecture that all quartic graphs have an even number of Hamiltonian circuit s. It is known that quartic graphs have an even number of Hamiltonian decomposition s. See also Cubic graph DEFAULTSORT Quartic Graph Category Graph families Category Regular graphs ... more details
In mathematics , and, in particular, in graph theory , a rooted graph is a graph mathematics mathematical graph in which one node graph theory node is labelled in a special way to distinguish it from the graph s other nodes. This special node is called the root of the graph. The number of rooted graphs for 1, 2, ... nodes is 1, 2, 6, 20, 90, 544, ... OEIS id A000666 A special case of interest are rooted tree s. External links http mathworld.wolfram.com RootedGraph.html MathWorld Rooted graph Combin stub Category Extensions and generalizations of graphs ... more details
A filter graph is used in multimedia processing. For example to capture video from a webcam . Filter software Filters take input, process it or change the input, and then output the processed data. An example of a filter, would be a video codec that takes raw uncompressed video and compresses it using a video standard such as H.264 . To compress a multimedia stream a filter graph could have two inputs Audio Video Usually these are expressed as file sources. The file sources would feed compression filters, the output of the compression filters would be fed to a multiplexer that would combine the two inputs and produce a single output. An example of a multiplexer would be an MPEG transport stream creator. Finally the multiplexer output would be fed to a file sink, which would create a file from the output. Image GStreamer Technical Overview.svg thumb center 500px GStreamer example of a filter graph. Image with inadequate rationale removed image dsmp3graph.gif thumb center 600px Filter graph of an mp3 file, as rendered by the DirectShow sample GraphEdit . The big boxes represent filters. A filter graph in multimedia processing is a directed graph . Edges represent one way data flow and nodes represent a data processing step. The term pins or pads are used to describe the connection point between nodes and edges. Example of programs that use filter graphs GStreamer Linux based multimedia framework. In Gstreamer a filter is called an element. Filter graphs can be built with the http gstreamer.freedesktop.org modules gst editor.html GStreamer Editor . GraphEdit Microsoft tool ... code for them. See also Explanation of filter graph in DirectShow article DirectShow Architecture External links DirectShow http www.gdcl.co.uk fgman.htm Explanation of filter graph manager http msdn2.microsoft.com ...&exp 0&select 1601363 Example of filter graph usage http msdn2.microsoft.com en us library ms783237.aspx Data Flow in the Filter Graph multimedia software stub Category Graphics software Category Multimedia ... more details
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