A Method for Computing the Wiener Index of One-Pentagonal Carbon Nanocones

The pentagonal carbon nanocones are constructed from a graphene sheet by removing a 60 ° wedge and joining the edges produces a cone with a single pentagonal defect at the apex. In this paper, the Wiener indices of these nanocones are computed generally by a new graph theoretical method, for the first time. We prove that our method is general and it is possible to apply for other nanostructures.