Extremal k*-cycle resonant hexagonal chains

Abstract

Denote by ℬ*n the set of all k*-cycle resonant hexagonal chains with n hexagons. For any Bn∈ℬ*n, let m(Bn) and i(Bn) be the numbers of matchings (= the Hosoya index) and the number of independent sets (= the Merrifield–Simmons index) of Bn, respectively. In this paper, we give a characterization of the k*-cycle resonant hexagonal chains, and show that for any Bn∈ℬ*n, m(Hn)≤m(Bn) and i(Hn)≥i(Bn), where Hn is the helicene chain. Moreover, equalities hold only if Bn=Hn.