An Exact Expression for the Szeged Index of V-Phenylenic Nanotubes and Nanotori

Abstract

Topological indices of nanotubes and nanotori are numerical descriptors that are derived from graphs of chemical compounds. The Szeged index is one of the most important topological indices defined in physico-chemistry. The Szeged index of the graph G is defined as Sz(G) Σuv=e∈E(G)Nu(e | G)Nv(e | G), where Nu(e | G) is the number of vertices of G lying closer to u and Nv(e | G) is the number of vertices of G lying closer to v. In this paper, Szeged index of V-phenylenic nanotubes and nanotori, are computed for first time.