Locally Petersen Graph

Author

Eric W. Weisstein
October 19, 2018

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

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

©2018 Wolfram Research, Inc. except for portions noted otherwise

Enumeration

TextGrid[Sort[{GraphData[#,"V"],#}&/@GraphData["LocallyPetersen"]],Dividers->All,Alignment->{{Decimal,Left}}]

Search

NeighborhoodGraph is really slow

EgoGraph[g_,i_]:=VertexDelete[NeighborhoodGraph[g,i],i]

Cases[Monitor[{g=#,Function[g,IsomorphicGraphQ[g,GraphData["PetersenGraph"]]]/@And@@Table[EgoGraph[GraphData[#],i],{i,GraphData[#,"V"]}]}&/@GraphData[2;;10],g],{g_,True}:>g]//Timing

Monitor[Select[GraphData[;;100],
Function[g,RecognizeGraph[
InduceSubgraph[
Graph[gg=g],
Flatten[Position[#,1]]
]]==="PetersenGraph"&/@(And@@Normal[GraphData[g,"DistanceMatrix"]])]],gg]//Timing

Monitor[Select[GraphData[All],
Function[g,RecognizeGraph[
InduceSubgraph[
Graph[gg=g],
Flatten[Position[#,1]]
]]==="PetersenGraph"&/@(And@@Normal[GraphData[g,"DistanceMatrix"]])]],gg]//Timing