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

摘要

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