Hyper-Wiener index of zigzag polyhex nanotubes

Abstract

The hyper-Wiener index of a connected graph G is defined as $WW(G)=(1/4)∑ (u,v) V(G)× V(G) (d(u,v)+d(u,v) ), where V (G) is the set of all vertices of G and d(u,v) is the distance between the vertices u,vV (G). In this paper we find an exact expression for the hyper-Wiener index of TUHC6[2p,q], the zigzag polyhex nanotube. Copyright © Australian Mathematical Society 2009.