Yu, Guihai; Feng, Lihua; Ilić, Aleksandar The hyper-Wiener index of trees with given parameters. (English) Zbl 1247.92068 Ars Comb. 96, 395-404 (2010). Summary: Let \(G\) be a connected graph. The hyper-Wiener index \(WW(G)\) is defined as \[ WW(G)=2^{-1}\sum _{u,v\in V(G)}d(u,v)+2^{-1}\sum _{u,v\in V(G)}d^2(u,v) \] with the summation going over all pairs of vertices in \(G\) and \(d(u,v)\) denotes the distance between \(u\) and \(v\) in \(G\). We determine the upper or lower bounds on the hyper-Wiener index of trees with given number of pendant vertices, matching number, independence number, domination number, diameter, radius and maximum degree. Cited in 7 Documents MSC: 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.) 05C90 Applications of graph theory 05C40 Connectivity 05C12 Distance in graphs Keywords:pendant vertices; matching number; diameter; maximum degree PDFBibTeX XMLCite \textit{G. Yu} et al., Ars Comb. 96, 395--404 (2010; Zbl 1247.92068)