Novel Face Index for Benzenoid Hydrocarbons

Abstract

A novel topological index, the face index ( F I ), is proposed in this paper. For a molecular graph G, face index is defined as F I ( G ) = ∑ f ∈ F ( G ) d ( f ) = ∑ v ∼ f , f ∈ F ( G ) d ( v ) , where d ( v ) is the degree of the vertex v. The index is very easy to calculate and improved the previously discussed correlation models for π - e l e c t r o n energy and boiling point of benzenoid hydrocarbons. The study shows that the multiple linear regression involving the novel topological index can predict the π -electron energy and boiling points of the benzenoid hydrocarbons with correlation coefficient r > 0.99 . Moreover, the face indices of some planar molecular structures such as 2-dimensional graphene, triangular benzenoid, circumcoronene series of benzenoid are also investigated. The results suggest that the proposed index with good correlation ability and structural selectivity promised to be a useful parameter in QSPR/QSAR.