1. The problem statement, all variables and given/known data Let G be a non-empty graph of order n whose vertices have degrees d1, . . . , dn. The line graph of G is defined as follows: the vertices of L(G) are the edges of G, and two vertices of L(G) are adjacent if they share an endpoint in G. Prove that the size of L(G) is: [tex]\sum(di choose 2)[/tex] from i=1 to n Hint: The size of Kd is (d choose 2) 2. Relevant equations 3. The attempt at a solution Well I know that the SUM(deg v)=2|E| meaning that |E| or the size of G is (1/2)SUM(di) Which would mean that the order of L(G) would be (1/2)SUM(di) I think that the line graph is a complete graph would would mean that would mean that the degree of each vertex would be (n-1), and in the case of the line graph would be ((1/2)SUM(di))-1 I don't really know if I'm on the right track, any help would be greatly appreciated!!!