Padmakar-Ivan index of TUC4C8(S) nanotubes

Abstract

A C4C8 net is a trivalent decoration made by alternating squares C-4 and octagons C-8. Such a covering can be derived from square net by the leapfrog operation. Stefu and Diudea recently computed the Wiener index of such nanotubes (see Monica Stefu and Mircea V. Diudea, MATCH-Commun. Math. Comput. Chem. 50, 133 (2004).). The Padmakar-lvan (PI) index of a graph G is defined as PI(G)=Sigma[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. This topological Index is developed very recently. In this paper, an exact expression for PI index of the TUC4C8(S) nanotubes is given.