Szeged index of TUC4C8(S) nanotubes

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Abstract

The Szeged index of a graph G is defined as Sz(G)=eE(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. In this paper we find an exact expression for Szeged index of 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]).

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