The Clar covering polynomial of hexagonal systems. III
type: Item
instance of: scholarly article
title: The Clar covering polynomial of hexagonal systems. III
zbMATH Open document ID: 0947.05077
DOI: 10.1016/S0012-365X(99)00293-9
author: Heping Zhang
author: Fuji Zhang
published in: Discrete Mathematics
publication date: 2000-11-08T00:00:00Z
review text: [For Part I see Discrete Appl. Math. 69, No. 1-2, 147-167 (1996; Zbl 0859.05070).] Let \(H\) be a hexagonal system with a perfect matching. A Clar cover of \(H\) is a spanning subgraph each component of which is either a hexagon or an edge. The set of hexagons in a Clar cover is a resonant pattern of \(H\) and a resonant pattern with the maximum number \(C(H)\) of hexagons is a Clar formula; \(C(H)\) is the Clar number. The sextet polynomial \(B(H,x)= \sum_n s(H, n)x^n\) where \(s(H,n)\) is the number of resonant patterns with \(n\) hexagons. The Clar covering polynomial \(P(H, w)= \sum_n\sigma(H, n)w^n\) where \(\sigma(H, n)\) is the number of Clar covers with \(n\) hexagons. In this paper a relation is etablished between these two polynomials, a lower bound for the Clar number is obtained and some properties of the Clar covering polynomial are deduced.
Mathematics Subject Classification ID: 05C90
Mathematics Subject Classification ID: 92E10
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 1421662
zbMATH Keywords: hexagonal system
zbMATH Keywords: perfect matching
zbMATH Keywords: Clar cover
zbMATH Keywords: resonant pattern
zbMATH Keywords: Clar formula
zbMATH Keywords: Clar number
zbMATH Keywords: sextet polynomial
zbMATH Keywords: Clar covering polynomial
reviewed by: E. Keith Lloyd
MaRDI profile type: Publication
Wikidata QID: Q127797946
full work available at URL: s0012-365x(99)00293-9
OpenAlex ID: W3020987526
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description: scientific article; zbMATH DE number 1421662