PI index of some benzenoid graphs

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, we first compute the PI index of a class of pericondensed benzenoid graphs consisting of n rows, n ≤ 3, of hexagons of various lengths. Finally, we prove that for any connected graph G with exactly m edges, PI(G) ≤ m(m-1) with equality if and only if G is an acyclic graph or a cycle of odd length. © 2006 Sociedad Chilena de Química.