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..

1. 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.