The wiener index of graphs of arbitrary girth and their line graphs
2010
We consider the invariant W(G) of a simple connected undirected graph G which is equal to the sum of distances between all pairs of its vertices in the natural metric (the Wiener index). We show that, for every g ≥ 5, there is a planar graph G of girth g satisfying W(L(G)) = W(G), where L(G) is the line graph of G.
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