I am currently trying to seek assistance in regards to graph isomorphism. I believe the graphs are indeed isomorphic as they both have 5 vertices, 5 edges and a degree of 2.
However, I just want to verify besides what I have mentioned is there anything else that I would need to look at to make sure these graphs are isomorphic? I believe you need to map each vertex in Graph 1 to the adjacent vertex in Graph 2 but I do need some assistance with that if anybody is willing to explain that part to me? I have attached a picture of the example also:
Let $G_1 = (V_1,E_1)$ and $G_2 = (V_2,E_2)$. You must define the isomorphism, which is a function $f : V_1 \rightarrow V_2$, respectively, and show that it satisfies the definition of a graph isomorphism, that is, that $f$ is a bijection and satisfies that if $\{ u,v\} \in E_1$, then $\{ f(u), f(v) \} \in E_2$. Hint: Let $f(e_1) = c_5$.