Find the number of vertices and edges of the line graph $\displaystyle L(G)$ of a graph $\displaystyle G$ with the degree

sequence $\displaystyle (d_1, d_2, . . . , d_n)$

The line graph of a graph $\displaystyle G$, denoted $\displaystyle L(G)$, is the graph with vertex set $\displaystyle E(G)$ in

which two vertices are adjacent if and only if the respective edges of $\displaystyle G$ have a vertex

in common.