# Count graphs with fixed number of vertices incluing isomorphisms [closed]

I'm trying to use the listgraph function in the Combinatorica package:

Needs["Combinatorica"]
g = ListGraphs[5];
ShowGraph /@ g


However, it only returns all the non-isomorphic graphs. Is it possible to return the isomorphic graphs as well, or at least count the number of isomorphic graphs for each graph?

• take a look at Automorphisms[ ] – Dr. belisarius Jul 14 '15 at 17:47
• Thanks. Yea I guess I could use Length[Automorphisms[ ]] for each element in g to count the degeneracies. – Zitao Wang Jul 14 '15 at 17:54
• Is there a way to generate graphs with the vertex labeling fixed? It seems that with ListGraphs the vertices are indistinguishable. For example, if I have v vertices, then there are $v \choose 2$ pairs of vertices, and the total number of graphs generated should be $2^{v \choose 2}$. – Zitao Wang Jul 14 '15 at 18:33
• Take a look at mathematica.stackexchange.com/a/60725/193 – Dr. belisarius Jul 14 '15 at 18:39
• – Dr. belisarius Jul 14 '15 at 18:39

Needs["Combinatorica"]