engleski

Reverse Wiener Indices of Graphs of Exactly Two Cycles

The reverse Wiener index of a connected graph G with n vertices is defined as A(G) =1/2n(n-1)d - W(G), where d and W(G) are respectively the diameter and Wiener index of G. We determine the n-vertex connected graph(s) of exactly two cycles of a vertex in common with the k-th greatest reverse Wiener indices for all k up to three if n = 7, four if n = 8, left perpendicular root n-7/2 right perpendicular + 1 if n >= 9, and the n-vertex connected graph(s) of exactly two vertex-disjoint cycles with the greatest reverse Wiener index. The n-vertex connected graphs with exactly two cycles with the greatest reverse Wiener index are determined for n >= 7.

reverse Wiener index ; Wiener index ; bicyclic graphs ; diameter

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