PI Index of Polyhex Nanotori

Abstract

The Padmakar–Ivan (PI) index of a graph G is defined as PI(G) = ¶[neu(e|G)+ nev(e|G)], where neu(e|G) is the number of edges of G lying closer to u than to v, nev(e|G) is the number of edges of G lying closer to v than to u and summation goes over all edges of G. In this paper, the PI index of a polyhex nanotorus T is computed. We prove that: