Document Type

Journal Article

Department/Unit

Department of Mathematics

Abstract

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 .

Publication Year

2003

Journal Title

Journal of Mathematical Chemistry

Volume number

33

Issue number

1

Publisher

Springer Verlag

First Page (page number)

17

Last Page (page number)

28

Referreed

1

DOI

10.1023/A:1023291329478

ISSN (print)

15728897

Link to Publisher’s Edition

https://dx.doi.org/10.1023/A:1023291329478

Keywords

k *-cycle resonant hexagonal chain, helicene chain, Hosoya index, Merrifield, Simmons index

Included in

Mathematics Commons

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