(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let G be a graph of order n and size m.

V(G)={v_{1},v_{2},...,v_{n}} and deg(v_{i})=r_{i}.

Find a formula for the size of the line graph L(G) in terms of n, m, and r_{i}.

2. Relevant equations

The http://en.wikipedia.org/wiki/Line_graph" [Broken] L(G) is the graph such that every vertex in L(G) corresponds to an edge in G, and two vertices in L(G) are adjacent iff the corresponding edges in G share a vertex.

3. The attempt at a solution

I know that the degree of any w in V(L(G)), when w is equivalent to some edge (v_{a},v_{b}) in G, is (r_{a}-1)+(r_{b}-1), that is to say r_{a}+r_{b}-2.

The size of L(G) would be (with it's vertices labeled from 1 to m).

[tex]

\frac{\sum_{i=1}^{m} r_{a_{i}}+r_{b_{i}}-2}{2}

[/tex]

Where v_{ai}and v_{bi}are the vertices of the edge in G corresponding to w_{i}in L(G). This, however, seems to be the least elegant solution possible. Is there a better solution? Are there any errors in the one I wrote? (I really am not sure about it).

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# Homework Help: [Graph theory] Formula for the size of a line graph

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