Szeged index of nanotubes

The Szeged index of a graph G is defined as S z ( G ) = ∑ e ∈ E ( G ) n u ( e ) n v ( e ) , where n u ( e ) is the number of vertices of G lying closer to u than to v , n v ( e ) is the number of vertices of G lying closer to v than to u and the summation goes over all edges e = u v of G . In this paper we find an exact expression for Szeged index of T U C 4 C 8 ( S ) nanotubes, using a theorem of A. Dobrynin and I. Gutman on connected bipartite graphs (see [A. Dobrynin, I. Gutman, On a graph invariant related to the sum of all distances in a graph, Publ. Inst. Math. Nouvelle ser. tome 56 (70) (1994) 18–22]).