The line graph $L(G)$ of a graph $G$ is defined in the following way: the vertices of $L(G)$ are the edges of $G$, $V(L(G)) = E(G)$, and two vertices in $L(G)$ are adjacent if and only if the corresponding edges in $G$ share a vertex.
The complement of $G$ is the graph $G$ whose node set is the same as that of $G$ and whose edge set consists of all the edges that are not in $E$.
a. Find the line graph $L(G)$ for the following graph http://gyazo.com/6bda20e850e58a9e240af71cded34c63
b. Find the complement of $L(K_5)$