Berlekamp-van Lint-Seidel Graph

Author

Eric W. Weisstein
October 3, 2025

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/Berlekamp-vanLint-SeidelGraph.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Berlekamp-vanLint-SeidelGraph.html.

©2025 Wolfram Research, Inc. except for portions noted otherwise

Relation to Koolen-Riebeek Graph

halves=HalvedGraphs[GraphData["KoolenRiebeekGraph"]]

IsomorphicGraphQ@@halves

RecognizeGraph[halves[[1]]]

RecognizeGraph[GraphComplement[halves[[1]]]]

Construction

distanceregular.org

g=DistanceRegularGraph["http://www.distanceregular.org/graphdata/bvls.am"]

VertexCount[g]

GraphDiameter[g]//Timing

RegularParameters[g]//Timing

DistanceRegularGraphQ[g]//Timing

IntersectionArray[g]//Timing

IntegerSpectrum[g]//SpectrumForm

GroupOrder[GraphAutomorphismGroup[g]]

HamiltonianGraphQ[g]

GraphData

GraphDataClassString

GraphDataClassString["BerlekampVanLintSeidelGraph"]

GraphDataString

VertexCount[g]

file=OpenWrite["~/berlekamp.m"]

WriteString[file,GraphDataString[g,
"StandardName"->"BerlekampVanLintSeidelGraph",
"Name"->"Berlekamp\[Hyphen]van Lint\[Hyphen]Seidel Graph",
"Embeddings"->None,
"Information"->"Berlekamp-vanLint-SeidelGraph",
"Classes"->{"DistanceRegular","DistanceTransitive","Noncirculant","Nongrid"},
Debug->True,
TimeConstraint->10]]

Close[file]