Extremal k*-cycle resonant hexagonal chains

Wai Chee Shiu; Peter Che Bor Lam; Lian-zhu Zhang

doi:10.1023/A:1023291329478

Extremal k*-cycle resonant hexagonal chains

Wai Chee Shiu^*, Peter Che Bor Lam, Lian-zhu Zhang

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

14 Citations (Scopus)

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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.

Original language	English
Pages (from-to)	17-28
Number of pages	12
Journal	Journal of Mathematical Chemistry
Volume	33
Issue number	1
DOIs	https://doi.org/10.1023/A:1023291329478
Publication status	Published - Jan 2003

Scopus Subject Areas

General Chemistry
Applied Mathematics

User-Defined Keywords

k*-cycle resonant hexagonal chain
Helicene chain
Hosoya index
Merrifield-Simmons index

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10.1023/A:1023291329478

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title = "Extremal k*-cycle resonant hexagonal chains",

abstract = "Denote by Bn* 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 ∈ Bn*, m(Hn) ≤ m(Bn) and i(Hn) ≥ i(Bn), where H n is the helicene chain. Moreover, equalities hold only if B n = Hn.",

keywords = "k*-cycle resonant hexagonal chain, Helicene chain, Hosoya index, Merrifield-Simmons index",

author = "Shiu, {Wai Chee} and Lam, {Peter Che Bor} and Lian-zhu Zhang",

note = "Funding Information: ∗ The work was partially supported by the Hong Kong Baptist University Faculty Research Grant; National Natural Science Foundation of China (No. 10271105).",

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T1 - Extremal k*-cycle resonant hexagonal chains

AU - Shiu, Wai Chee

AU - Lam, Peter Che Bor

AU - Zhang, Lian-zhu

N1 - Funding Information: ∗ The work was partially supported by the Hong Kong Baptist University Faculty Research Grant; National Natural Science Foundation of China (No. 10271105).

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N2 - Denote by Bn* 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 ∈ Bn*, m(Hn) ≤ m(Bn) and i(Hn) ≥ i(Bn), where H n is the helicene chain. Moreover, equalities hold only if B n = Hn.

AB - Denote by Bn* 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 ∈ Bn*, m(Hn) ≤ m(Bn) and i(Hn) ≥ i(Bn), where H n is the helicene chain. Moreover, equalities hold only if B n = Hn.

KW - k-cycle resonant hexagonal chain

KW - Helicene chain

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KW - Merrifield-Simmons index

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JF - Journal of Mathematical Chemistry

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Extremal k*-cycle resonant hexagonal chains

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