Abstract
The reciprocal reverse Wiener index R?(G) of a connected graph G is defined in mathematical chemistry as the sum of weights 1/d(G)?dG(u,v) of all unordered pairs of distinct vertices u and v with dG(u, v) < d(G), where dG(u, v) is the distance between vertices u and v in G and d(G) is the diameter of G. We determine the minimum and maximum reciprocal reverse Wiener indices in the class of n-vertex unicyclic graphs and characterize the corresponding extremal graphs.
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