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

Abstract

The Padmakar–Ivan (PI) index of a graph G is defined as PI $$(G) = \Sigma [n_{\rm eu}(e\vert G)+n_{\rm ev}(e\vert G)]$$ , where for edge e=(u,v) are $$n_{\rm eu} (e\vert G)$$ the number of edges of G lying closer to u than v, and $$n_{\rm ev} (e\vert G)$$ 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.