The wiener index of graphs of arbitrary girth and their line graphs |
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| Authors: | A A Dobrynin |
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| Institution: | (2) Division of Material Sciences, Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Japan; |
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| Abstract: | 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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