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The hyper-Wiener index of trees with given parameters. (English) Zbl 1247.92068

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.

MSC:

92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
05C90 Applications of graph theory
05C40 Connectivity
05C12 Distance in graphs
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