Mathon Graph

Author

Eric W. Weisstein
April 16, 2021

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

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

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

Sources

Brouwer, A. E. and van Lint, J. H. §6.D in "Strongly Regular Graphs and Partial Geometries." In Enumeration and design (Waterloo, Ont., 1982). Toronto, Canada: Academic Press, pp. 85-122, 1984.
Cohen, N. and Pasechnik,  D. V. "Implementing Brouwer's Database of Strongly Regular Graphs." 20 Jul 2016. https://arxiv.org/abs/1601.00181.
Hollmann, H. D. L. "Association Schemes." MSc. thesis. Eindhoven, Netherlands: Eindhoven University of Technology, 1982.

Graphs

GraphData["Mathon"]

GraphData[#,"VertexCount"]&/@GraphData["Mathon"]

DeleteCases[Show[GraphData[#],PlotLabel->GraphData[#,"Name"]]&/@With[{class="Mathon"},Sort[{Lookup[GraphData[#,"NotationRules"],class],#}&/@GraphData[class]]][[All,2]],_Show]

Special cases

With[{class="Mathon"},TextGrid[Sort[{Lookup[GraphData[#,"NotationRules"],class],GraphData[#,"V"],#}&/@GraphData[class]],Dividers->All,Alignment->{{Left,Decimal,Left}}]]

Construction

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

0

from sage.graphs.generators.smallgraphs import MathonStronglyRegularGraph
g = MathonStronglyRegularGraph(0) ;
g.edges()

g0=SageGraph@;

RegularParameters[g0]//Timing

RecognizeGraph[g0]

1

from sage.graphs.generators.smallgraphs import MathonStronglyRegularGraph
g = MathonStronglyRegularGraph(1) ;
g.edges()

g1=SageGraph@;

RegularParameters[g1]//Timing

RecognizeGraph[g1]

2

from sage.graphs.generators.smallgraphs import MathonStronglyRegularGraph
g = MathonStronglyRegularGraph(2) ;
g.edges()

g2=SageGraph@;

RegularParameters[g2]//Timing

RecognizeGraph[g2]

Properties

TextGrid[{#1,IntegerSpectrum[#2]//SpectrumForm,Flatten@RegularParameters[#2]}&@@@Transpose[{{0,1,2},{g0,g1,g2}}],Dividers->All]

GraphData

GraphDataClassString

GraphDataClassString[g]

GraphDataString

<<MathWorld`Graphs`

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

Do[WriteString[file,GraphDataString[{g0,g1,g2}[[i+1]],
"StandardName"->{"Mathon",i},
"Name"->Switch[i,0,"zeroth",1,"first",2,"second"]<>" Mathon graph",
"Information"->"MathonGraphs",
"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,0,2}]

Close[file]