# Number of isomorphic graphs for a particular digraph

Suppose we have a simple digraph $G$ with $g$ vertices and $a$ arcs. How should one count all graphs in that isomorphism class (i.e., all graphs isomorphic to graph $G$).

Any pointers would be really appreciated.

-

So really you are looking for the set of permutations of the labels which result in distinct labellings. E.g. for the directed claw $a\rightarrow b$, $a\rightarrow c$, $a\rightarrow d$, any permutation of the labels $b,c,d$ give the same labeled digraph, and any digraph with a different root of the claw with be nonisomorphic. In this example it seems that there are only 4 distinct labeled digraphs.