Topological lattice descriptors of graphene sheets with fullerene-like nanostructures

Abstract

Abstract Polynomial behaviour of the Wiener index for infinite chemical graphs is subject here to a generalisation to structures with topological dimensionality d T>1. This allows a pure topological analysis of relative chemical stability of graphite lattice portions and fullerene fragments (nanocones) built around a pentagonal face. The Wiener index of the graph acts as a lattice topological potential subject to a minimum principle that is able to discriminate topological structures made of hexagons with different connectivity. A new indicator of graph topological efficiency has been applied in the infinite lattice limit to allow a complete ranking of graph chemical stability. A certain grade of reactivity of the pentagonal ring at the centre of nanocones is also predicted. Our considerations are mainly performed in the dual topological space. Keywords: topological Wiener indexcarbon blackfullerenescarbon nanostructure Acknowledgements We wish to thank Prof. Gianni Strazzulla for his helpful discussion. We wish to acknowledge ASI, the Italian Space Agency, for the partial support of the present work under the Contract No. I/015/07/0 (Studi di Esporazione del Sistema Solare).