A relation between clar covering polynomial and cube polynomial

Heping Zhang; Wai Chee Shiu; Pak Kiu Sun

A relation between clar covering polynomial and cube polynomial

Heping Zhang, Wai Chee Shiu^*, Pak Kiu Sun

^*Corresponding author for this work

Department of Mathematics

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

21 Citations (Scopus)

Abstract

The Clar covering polynomial (Zhang-Zhang polynomial) of a hexagonal system is a counting polynomial of resonant structures called Clar covers, which can be used to determine the Kekulé count, the first Herndon number and Clar number. In this paper we prove that the Clar covering polynomial of a hexagonal system H coincides with the cube polynomial of its resonance graph R(H) by establishing a bijection between the Clar covers of H and the hypercubes in R(H). Moreover, some important applications of this relation are presented.

Original language	English
Pages (from-to)	477-492
Number of pages	16
Journal	MATCH Communications in Mathematical and in Computer Chemistry
Volume	70
Issue number	2
Publication status	Published - 2013

Scopus Subject Areas

General Chemistry
Computer Science Applications
Computational Theory and Mathematics
Applied Mathematics

Cite this

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title = "A relation between clar covering polynomial and cube polynomial",

abstract = "The Clar covering polynomial (Zhang-Zhang polynomial) of a hexagonal system is a counting polynomial of resonant structures called Clar covers, which can be used to determine the Kekul{\'e} count, the first Herndon number and Clar number. In this paper we prove that the Clar covering polynomial of a hexagonal system H coincides with the cube polynomial of its resonance graph R(H) by establishing a bijection between the Clar covers of H and the hypercubes in R(H). Moreover, some important applications of this relation are presented.",

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AU - Zhang, Heping

AU - Shiu, Wai Chee

AU - Sun, Pak Kiu

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N2 - The Clar covering polynomial (Zhang-Zhang polynomial) of a hexagonal system is a counting polynomial of resonant structures called Clar covers, which can be used to determine the Kekulé count, the first Herndon number and Clar number. In this paper we prove that the Clar covering polynomial of a hexagonal system H coincides with the cube polynomial of its resonance graph R(H) by establishing a bijection between the Clar covers of H and the hypercubes in R(H). Moreover, some important applications of this relation are presented.

AB - The Clar covering polynomial (Zhang-Zhang polynomial) of a hexagonal system is a counting polynomial of resonant structures called Clar covers, which can be used to determine the Kekulé count, the first Herndon number and Clar number. In this paper we prove that the Clar covering polynomial of a hexagonal system H coincides with the cube polynomial of its resonance graph R(H) by establishing a bijection between the Clar covers of H and the hypercubes in R(H). Moreover, some important applications of this relation are presented.

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M3 - Journal article

AN - SCOPUS:84898756060

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SP - 477

EP - 492

JO - MATCH Communications in Mathematical and in Computer Chemistry

JF - MATCH Communications in Mathematical and in Computer Chemistry

IS - 2

ER -

A relation between clar covering polynomial and cube polynomial

Abstract

Scopus Subject Areas

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