Let $G$ be a graph, the line graph of $G$ denoted of $L(G)$ is defined as follows:
-The vertices of $L(G)$ are the edges of $G$
-Two vertices of $L(G)$ are adjacent iff their corresponding edges in $G$ are incident G.
It is easy to see that if $G$ is $d$-regular graph then $L(G)$ is $(2d-2)$-regular graph. Thus $2d-2$ is eigenvalue of $L(G)$.
Let $G$ be $d$-regular graph. Is there any relation between the eigenvalues of $L(G)$ and those of $G$?