Delsarte Graph

Author

Eric W. Weisstein
March 4, 2021

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

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

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

Source

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

Construction

g=DistanceRegularGraph["delsarte"]

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=OpenWrite["~/delsarte.m"]

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

Close[file]