Szeged index of TUC4C8(S)TUC4C8(S) nanotubes

The Szeged index of a graph GG is defined as Sz(G)=∑e∈E(G)nu(e)nv(e)Sz(G)=∑e∈E(G)nu(e)nv(e), where nu(e)nu(e) is the number of vertices of GG lying closer to uu than to vv, nv(e)nv(e) is the number of vertices of GG lying closer to vv than to uu and the summation goes over all edges e=uve=uv of GG. In this paper we find an exact expression for Szeged index of TUC4C8(S)TUC4C8(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]).