Games Graph

Author

Eric W. Weisstein
March 4, 2021

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/GamesGraph.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/GamesGraph.html.

©2021 Wolfram Research, Inc. except for portions noted otherwise

Source

https://www.distanceregular.org/graphs/games.html

Construction

g=DistanceRegularGraph["games"]

RecognizeGraph[g]

Properties

VertexCount[g]

GraphDiameter[g]

RegularParameters[g]

IntersectionArray[g]//Timing

<<IGraphM`

IGIntersectionArray[g]

IntegerSpectrum[g]//SpectrumForm

DistanceRegularGraphQ[g]//Timing

DistanceTransitiveGraphQ[g]//Timing

GraphData

GraphDataClassString

GraphDataClassString[g]

GraphDataString

file=OpenAppend["~/dr.m"]

WriteString[file,GraphDataString[g,
"StandardName"->"GamesGraph",
"Name"->"Games graph",
"Information"->"GamesGraph",
"Embeddings"->{},
"Skip"->{"Arboricity","BurningNumber","Chord","ChordlessCycle","ChordlessCycles","Chords","ChromaticNumber","CliqueCoveringNumber","ComplementOddChordlessCycle","ComplementOddChordlessCycles","ConnectedInducedSubgraphPolynomial","ConnectedInducedSubgraphs","CrossingNumber","Cycles","CyclePolynomial","DominatingSet","DominatingSets","EdgeCovers","GracefulLabeling","GracefulLabelings","HamiltonianCycles","HamiltonianPaths","HamiltonianWalks","IdiosyncraticPolynomial","IndependentVertexSets","LongestCycles","MatchingGeneratingPolynomial","MaximalIndependentEdgeSets","MaximalIndependentVertexSets","MaximallyNonhamiltonian","MaximumFlowMatrix","MaximumIndependentEdgeSets","MinimumCoveringsByMaximalCliques","MinimumEdgeColoring","MinimumVertexColoring","MinimumVertexCut","MinimumVertexCuts","MinimumWeightFractionalColoring","MinimumWeightFractionalEdgeColoring","OddChordlessCycles","PathPolynomial","Paths","RadioLabeling","RadioLabelings","RadioNumber","RectilinearCrossingCount","ResistanceMatrix","Skewness","StronglyPerfect","UnitDistance","Thickness"},
TimeConstraint->10
]]

Close[file]