Polynema

Author

Eric W. Weisstein
June 3, 2004

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

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

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

Code

Polynemas[n_]:=Select[Flatten[ConnectedGraphs/@Range[n+1]],M[#]==n&]

Enumeration

Length/@(poly=Polynemas/@Range[6])//Timing

poly[n_]:=RootedEmbedding[#,1]&/@Select[Flatten[Table[AllGraphs[i],{i,n+1}]],ConnectedQ[#]&&M[#]==n&]

Timing[Length/@Table[poly[i],{i,6}]]

ShowGraphArray[Flatten[Partition[#,6,6,{1,1},{}]&/@Map[RootedEmbedding[#,1]&,
Take[poly,5],
{2}],1],
VertexStyle->Disk[.1],GraphicsSpacing->{.5,.4}
]