A complete characterization for \(k\)-resonant Klein-bottle polyhexes
type: Item
instance of: scholarly article
title: A complete characterization for \(k\)-resonant Klein-bottle polyhexes
zbMATH Open document ID: 1148.05031
author: Wai Chee Shiu
author: Heping Zhang
publication date: 2008-05-21T00:00:00Z
review text: A toroidal polyhex is a 3-regular bipartite graph imbedded in the torus with all faces hexagonal. A hexagonal tessellation \(K(p,q,t)\) on the Klein bottle is a finite-sized elemental benzenoid which can be obtained from a hexagonal lattice on a \(p\times q\)-parallelogram with the usual identification of sides and torsion \(t\). A polyhex is \(k\)-resonant if for each positive integer \(i\) at most \(k\), any \(i\) disjoint hexagons are alternating hexagons with respect to a certain perfect matching. Unlike the toroidal polyhex, \(K(p,q,t)\) is not transitive (except for some degenerate cases). The authors show, however, that \(K(p,q,t)\) is independent of \(t\); they give criteria for \(K(p,q,t)\) to be \(k\)-resonant for every positive integer \(k\), and they show that the \(K(p,q,t)\) of 3-resonance are fully benzenoid.
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05C90
zbMATH DE Number: 5277674
zbMATH Keywords: fullerene
zbMATH Keywords: Klein bottle polyhex
zbMATH Keywords: toroidal polyhex
zbMATH Keywords: Kekulé structure
zbMATH Keywords: \(k\)-resonance
reviewed by: Arthur T. White
MaRDI profile type: Publication
full work available at URL: s10910-006-9178-6
OpenAlex ID: W2063528026
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DOI: 10.1007/S10910-006-9178-6
published in: Journal of Mathematical Chemistry
description: scientific article; zbMATH DE number 5277674