Pentagonal 3-polytopal graphs with edges of only two types and shortness parameters
type: Item
instance of: scholarly article
title: Pentagonal 3-polytopal graphs with edges of only two types and shortness parameters
zbMATH Open document ID: 0823.05035
DOI: 10.1016/0012-365X(93)E0141-P
author: Peter J. Owens
author: Stanislav Jendroľ
published in: Discrete Mathematics
publication date: 1995-10-08T00:00:00Z
review text: For a graph \(G\), let \(h(G)\) denote the length of a maximum cycle of \(G\). For an infinite class of graphs, \(\mathcal G\), the shortness exponent \(\sigma({\mathcal G})\) and the shortness coefficient \(\rho({\mathcal G})\) are defined by \[ \sigma({\mathcal G})= \lim \inf_{G\in {\mathcal G}} {\log h(G)\over \log| V(G)|}\quad\text{and}\quad \rho({\mathcal G})= \lim \inf_{G\in {\mathcal G}} {h(G)\over | V(G)|}. \] This paper considers the class of pentagonal 3-polytopal graphs all of whose edges are incident either with two 3-valent vertices or with a 3-valent vertex and a \(q\)-valent vertex. For most values of \(q\), the authors show that the shortness exponent of the class and the shortness coefficient of a special class are less than one. For \(q= 4\), they find a positive lower bound for the shortness coefficient.
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 719464
zbMATH Keywords: maximum cycle
zbMATH Keywords: shortness exponent
zbMATH Keywords: shortness coefficient
reviewed by: Alan C. Tucker
MaRDI profile type: Publication
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Wikidata QID: Q126982431
description: scientific article; zbMATH DE number 719464