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 .
Journal of Mathematical Chemistry
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k *-cycle resonant hexagonal chain, helicene chain, Hosoya index, Merrifield, Simmons index
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.