Hyper Wiener index of zigzag polyhex nanotubes

Abstract

The hyper Wiener index of a connected graph $G$ is defined as $WW(G)=\frac{1}{2}\sum_{\{u,v\}\subseteq V(G)}\bigg(d(u,v)+\frac{1}{2}(d(u,v))^2\bigg)$, where $V(G)$ is the set of all vertices of $G$ and $d(u,v)$ is the distance between the vertices $u,v\in V(G)$. In this paper we find an exact expression for hyper Wiener index of $TUHC_6[2p,q]$, the zigzag polyhex nanotube. doi:10.1017/S1446181108000278