Luo, Wei; Zhou, Bo; Trinajstić, Nenad; Du, Zhibin Reverse Wiener indices of graphs of exactly two cycles. (English) Zbl 1256.05060 Util. Math. 88, 189-202 (2012). Summary: The reverse Wiener index of a connected graph \(G\) with \(n\) vertices is defined as \(\Lambda(G)= {1\over 2} n(n-1)d- W(G)\), 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 \(n=8\), \(\left\lfloor{\sqrt{n-7}\over 2}\right\rfloor+ 1\) if \(n\geq 9\), 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 \(n\geq 7\). Cited in 1 Document MSC: 05C12 Distance in graphs 05C38 Paths and cycles 05C40 Connectivity Keywords:greatest reverse Wiener index; two vertex-disjoint cycles; bicyclic graphs; diameter; connected graph PDFBibTeX XMLCite \textit{W. Luo} et al., Util. Math. 88, 189--202 (2012; Zbl 1256.05060)