# How to know if two graphs are ismorphic or not?

For example in the picture above.

I know that I need to calculate if both graphs have the same number of vertices and edges.

But I don't know what I should do next to check if the graphs are isomorphic or not.

• The original title reminded me of this story. Jan 15 '16 at 15:08

Graph isomorphisms preserve the vertex degree, that is, the number of edges incident to a vertex. In $G'$, the vertex $w_5$ has degree $5$, but there is no vertex with degree $5$ in $G$. Thus, the graphs cannot be isomorphic.