Department of Mathematics
Denote by ℬ* n the set of all k *-cycle resonant hexagonal chains with n hexagons. For any B n ∈ℬ* n , let m(B n ) and i(B n ) be the numbers of matchings (= the Hosoya index) and the number of independent sets (= the Merrifield–Simmons index) of B n , respectively. In this paper, we give a characterization of the k *-cycle resonant hexagonal chains, and show that for any B n ∈ℬ* n , m(H n )≤m(B n ) and i(H n )≥i(B n ), where H n is the helicene chain. Moreover, equalities hold only if B n =H n .
k *-cycle resonant hexagonal chain, helicene chain, Hosoya index, Merrifield, Simmons index
Source Publication Title
Journal of Mathematical Chemistry
Link to Publisher's Edition
Shiu, Wai Chee, Peter Che Bor Lam, and Lian-zhu Zhang. "Extremal k*-cycle resonant hexagonal chains." Journal of Mathematical Chemistry 33.1 (2003): 17-28.