Szeged and Balaban indices of zigzag polyhex nanotubes

Abstract

The Sezegd index of a graph G is defined as Sz(G)= Σ eεE(G) nu(e)nv(e), where nu(e) is the number of vertices of G lying closer to u than to v, nv(e) is the number of vertices of G lying closer to v than to u and the summation goes over all edges e = uv of G. Also Balaban index of G is defined by J(G) = m/(μ + 1) ΣuvεE(G) [d(u)d(v)]-0.5, where d(v) = ΣxεV(G) d(v, x), is the summation of distances between v and all vertices of G, m is the number of edges in G and μ is the cyclomatic number of G. In this paper we find an exact expression for Szeged and Balaban indices of TUHC6[2p, q], the zigzag polyhex nanotubes, using a theorem of Dobrynin and Gutman on connected bipartite graphs (see Ref [11]).