Janko-Kharaghani Graphs

Author

Eric W. Weisstein
March 17, 2021

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/Janko-KharaghaniGraphs.nb.

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

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

Source

Peter B. Gibbons and Rudolf Mathon. Construction methods for Bhaskar Rao and related designs. J. Austral. Math. Soc. Ser. A 42 (1987), no. 1, 5–30. http://journals.cambridge.org/article_S1446788700033929

Zvonimir Janko and Hadi Kharaghani. A Block Negacyclic Bush-Type Hadamard Matrix and Two Strongly Regular Graphs. J. Combin. Theory Ser. A 98 (2002), no. 1, 118–126. doi:10.1006/jcta.2001.3231

Construction

https://doc.sagemath.org/html/en/reference/graphs/sage/graphs/graph_generators.html#sage.graphs.graph_generators.GraphGenerators.JankoKharaghaniGraph

936

g1=SageGraph[SageEvaluate["graphs.JankoKharaghaniGraph(936).edges()"]]

RegularParameters[g1]//Timing

RecognizeGraph[g1]

cf=CanonicalForm[];//Timing

1800

Too large

g2=SageGraph[SageEvaluate["graphs.JankoKharaghaniGraph(1800).edges()"]]

Through[{VertexCount,EdgeCount}[g]]

RegularParameters[g2]

RecognizeGraph[g2]

GraphData

GraphDataClassString

GraphDataClassString[g]

GraphDataString

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

Do[WriteString[file,GraphDataString[g={g1,g2}[[i]],
"StandardName"->"JankoKharaghaniGraph"<>ToString[VertexCount[g]],
"Name"->ToString[VertexCount[g]]<>"\[Hyphen]Janko\[Hyphen]Kharaghani graph",
"Information"->"JankoKharaghaniGraphs",
"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","VertexCover","Thickness"},
TimeConstraint->10
]],{i,{2}}]