1. ## Isomorphic graphs

Two of the following graphs are isomorphic and one is not .Identify the non isomorphic graph and provide a clear argument why the 3rd one is not to the other two.

I understand graphs are Isomorphic if they have the same number of vertices and edges ,The same degree sequence ,the same cycles ,the same number of components ,articulation points and the same diameter.would G3 be non isomorphic as it has more paths ?

2. ## Re: Isomorphic graphs

A graph need not be drawn the same way it is shown
You may move the vertices to a different position so long as it keeps the same edges and you have the same graph. The definition of a graph is a set of vertices and a set of edges. In G3, what happens if you swap the positions of the middle two vertices while keeping all the same edges? It looks exactly like G1. The one that is not isomorphic is G2. Label the vertices of G1 and G3 and find a bijective mapping that preserves edges. Show that G2 has cycles of length 3, but neither G1 nor G3 does.