An Exact Expression for the Padmakar-Ivan Polynomial of Some Nanostructures

The Padmakar-Ivan (PI) index of a molecular graph G is defined as PI(G) = Sigma(e is an element of G)[n(eu)(e vertical bar G) + n(ev) (e vertical bar G)], where n(eu)(e vertical bar G) is the number of edges of G lying closer to u than to v, n(ev) (e vertical bar G) is the number of edges of G lying closer to v than to u and summation goes over all edges of G. The PI polynomial of a chemical graph is defined by present authors to investigate some physico-chemical properties of nanotubes. In this paper, the PI polynomial of a polyhex nanotube is computed.