Topological lattice descriptors of graphene sheets with fullerene-like nanostructures

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.

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