The Reciprocal Reverse Wiener Index of Unicyclic Graphs

The reciprocal reverse Wiener index R Lambda(G) of a connected graph G is defined in mathematical chemistry as the sum of weights 1/d(G)-d(G)(u,v) of all unordered pairs of distinct vertices u and v with d(G)(u,v) < d(G), where d(G)(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.