Conference Graph

Author

Eric W. Weisstein
February 1, 2008

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

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

©2008 Wolfram Research, Inc. except for portions noted otherwise

Enumeration

ConferenceGraphQ[spec_,parms_]:=Module[{s=s=Length/@Split[DeleteCases[spec,parms[[2]]]]},
Length[s]==2&&Equal@@s
]

l=Select[GraphData["StronglyRegular"],Length[s=Length/@Split[DeleteCases[GraphData[#,"Spectrum"],("StronglyRegular"/.GraphData[#,"NotationRules"])[[2]]]]]==2&&Equal@@s&]

l=GraphData["Conference"]

TableForm[Sort[{GraphData[#,"V"],#,"StronglyRegular"/.GraphData[#,"NotationRules"],GetGraphData[#,"CharacteristicPolynomial"][x]/.Times[-1,x__]:>Times[x]}&/@l],TableDepth->2]//TraditionalForm

RecognizeGraph[LineGraph[CompleteGraph[3,3]]]

"Paley"/.GraphData[{"GeneralizedQuadrangle",{2,1}},"NotationRules"]