If $G$ is a cycle, then $G \simeq L(G)$.
In the line graph of $C_n$, vertex $e_1$ adjecent to $e_n$ and $e_2$, ..., vertex $e_n$ adjecent to $e_1$ and $e_{n-1}$. I am getting a cyclic graph with n vertices.For me the given result is trivial. How do I write the formal proof?