Symmetric Graph

Author

Eric W. Weisstein
May 16, 2017

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

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

©2017 Wolfram Research, Inc. except for portions noted otherwise

Count

Connected

A133181

Table[Total[Boole[SymmetricGraphQ/@ConnectedGraphs[n]]],{n,10}]//Timing

Table[Length@GraphData[{"Symmetric","Connected"},n],{n,12}]

Disconnected

A087145

Table[Length@GraphData[{"Symmetric","Disconnected"},n],{n,12}]

All

A286931

Table[Total[Boole[SymmetricGraphQ/@Graphs[n]]],{n,10}]//Timing

Table[Length@GraphData["Symmetric",n],{n,10}]

Figure

Connected

s=Table[GraphData["Symmetric",n],{n,7}]

GraphicsGrid[Map[GraphData[#,"Image"]&,DeleteCases[s,{}],{2}],Dividers->All]

s=Table[GraphData["Symmetric",n],{n,8}]

Length/@s

GraphicsGrid[Map[GraphData[#,"Image"]&,DeleteCases[s,{}],{2}],Dividers->All]

Disconnected

s=Table[GraphData[{"Symmetric","Disconnected"},n],{n,9}]

GraphicsGrid[Map[GraphData[#,"Image"]&,DeleteCases[s,{}],{2}],Dividers->All]