Line graph of a graph G is a graph in which every edge in is represented with a vertex. Two vertices in are adjacent if and only if the corresponding edges in G share a vertex.
Now suppose graph G has vertices, labeled and the degree of each vertex is .
Find the size of .
I have attempted to solve it, but I'm stuck.
The order of is . Let's call it m.
The vertex is the edge from some vertex to another , it's degree is therefore .
While I'm quite sure this is correct, it doesn't seem to be very useful - or indeed the expected answer. Any help?