Counting Graph Isomorphism

Question

I am self studying graph theory and was wondering: is there a simple way to count/compute the number of subgraphs G that are isomorphic to another graph (say, G')?

For instance, if G = the complete graph "K_10" with 10 vertices, and G' = Hypercube H_3 with 3 vertices

Or, if G = Hypercube "H_4" with 4 vertices, and G' = Complete biparite graph "K_1, 3".

Answer 1

If $G$ is a complete graph, and the vertices of $G'$ are labelled, it's easy, because you can use any one-to-one mapping of the vertices of $G'$ into the vertices of $G$. If the vertices of $G'$ are not labelled, you'll want to divide by the number of automorphisms of $G'$.