Abstract

The Wiener index of a molecular graph G is defined as the summation of topological distances between all pair of atoms in G. In this paper an algorithm by Sandi Klavzar [European J. Combin. 2006, 27, 68 – 73] is applied to calculate the Wiener index of one-heptagonal nanocone L[n]. It is proved that W(L[n]) = (238/5)n5 + (238)n4 + (2821/6)n3 + (917/2)n2 + (3311/15)n + 42.

Keywords: Carbon nanocone, Djokovic-Winkler relation, molecular graph, one-heptagonal nanocone, topological index, Wiener index.