A Method of Computing the PI Index of Benzenoid Hydrocarbons Using Orthogonal Cuts

The Padmakar-Ivan (PI) index of a graph G is defined as PI (G) = Σ [neu(e|G)+nev(e|G)], where for edge e=(u,v) are neu (e|G) the number of edges of G lying closer to u than v, and nev (e|G) is the number of edges of G lying closer to v than u and summation goes over all edges of G. The PI index is a Wiener-Szeged-like topological index developed very recently. In this paper we describe a method of computing PI index of benzenoid hydrocarbons (H) using orthogonal cuts. The method requires the finding of number of edges in the orthogonal cuts in a benzenoid system (H) and the edge number of H - a task significantly simpler than the calculation of PI index directly from its definition