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

John, Peter E. GND; Khadikar, Padmakar V.; Singh, Jyoti

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.

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John PD Dr. rer. nat. habil., P.E., Khadikar, P.V., Singh, J., 2006. A Method of Computing the PI Index of Benzenoid Hydrocarbons Using Orthogonal Cuts. Preprint /  Technische Universität Ilmenau, Institut für Mathematik, Preprint /  Technische Universität Ilmenau, Institut für Mathematik 06–04.
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