PI Index of Armchair Polyhex Nanotubes

Abstract

The Padmakar-Ivan (PI) index of a graph $G$ is defined as $PI(G)=\sum [n_{eu}(e|G)+n_{ev}(e|G)]$ where $n_{eu}(e|G)$ is the number of edges of $G$ lying closer to $u$ than to $v$, $n_{ev}(e|G)$ is the number of edges of $G$ lying closer to $v$ than to $u$, and the summation goes over all edges of $G$. The PI Index is a Szeged-like topological index developed very recently. In this paper, an exact expression for the PI index of the armchair polyhex nanotubes is given.