Some new researches on the general connectivity index of benzenoid systems

Abstract

Given H a benzenoid system, we find an expression of the general connectivity index, denoted by χ α (H), in terms of inlet features and internal vertex features of H. As a consequence, the extremal n-benzenoid systems with maximal general connectivity index χ α are completely characterized. Moreover, by constructing a combinatorial bijection, we prove that the linear chain L n is the unique extremal n-benzenoid system with minimal general connectivity index χ α if and only if α>α ∗, where α ∗ is the positive root of the equation 2×6 x −9 x =0.