Generalized Moore Graph

Author

Eric W. Weisstein
October 24, 2003

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

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

©2005 Wolfram Research, Inc. except for portions noted otherwise

Enumeration

Timing[Length/@(gmg=Select[Graphs[#],GeneralizedMooreGraphQ]&/@Range[9])]

Off[General::"stop"]

ShowGraphArray[Flatten[Partition[#,7,7,{1,1},{}]&/@Map[RecognizeGraph,
DeleteCases[Take[gmg,8],{}],
{2}],1],AspectRatio->Automatic,VertexStyle->Disk[.08]]

Cubic Generalized Moore Graphs

Timing[Length/@(cubic=Select[#,CubicQ]&/@gmg)]

Off[General::"stop"]

ShowGraphArray[Map[RecognizeGraph,
DeleteCases[cubic,{}],
{2}],AspectRatio->Automatic,VertexStyle->Disk[.06]]