How many graphs are there with 5 vertices up to isomorphism

How many graphs are there with 5 vertices, up to isomorphism?

show all the graphs

Solution

Let us call graphs G=(V,E)G=(V,E) and G=(V,E)G=(V,E) fundamentally different if they are not isomorphic. How many fundamentally different graphs are there on four vertices?

This is a question on my homework. I\'m thinking that I need to exhaust all the possible variations of a graph with four vertices:

Each vertices could have a degree of 0, 1, 2 or 3,4.

Four possibilities times 5 vertices = 32 possibilities.

And also, maybe, since the graphs are fundamentally different (not isomorphic), you need to minus 1 possible variation since it would match the other graph.