The hyper-Wiener index of graph operations

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Abstract

Let G be a graph. The distance d(u,v) between the vertices u and v of the graph G is equal to the length of a shortest path that connects u and v. The Wiener index W(G) is the sum of all distances between vertices of G, whereas the hyper-Wiener index WW(G) is defined as WW(G)=12W(G)+12{u,v}V(G)d(u,v)2. In this paper the hyper-Wiener indices of the Cartesian product, composition, join and disjunction of graphs are computed. We apply some of our results to compute the hyper-Wiener index of C4 nanotubes, C4 nanotori and q-multi-walled polyhex nanotori.

Keywords

Hyper-Wiener index
Graph operations
C4 nanotube
C4 nanotorus
q-multi-walled nanotube

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