Novel face index for benzenoid hydrocarbons

A novel topological index, the face index (FI), is proposed in this paper. For a molecular graph G, face index is defined as FI(G) = Σ_f∈F(G) d(f) = Σ_{υ~f, f∈F(G)} d(υ), where d(υ) is the degree of the vertex υ. The index is very easy to calculate and improved the previously discussed correlation models for π-electron 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.