Edge-connectivity of regular graphs with two orbits
type: Item
instance of: scholarly article
title: Edge-connectivity of regular graphs with two orbits
zbMATH Open document ID: 1153.05033
author: Fengxia Liu
author: Jixiang Meng
published in: Discrete Mathematics
publication date: 2008-07-11T00:00:00Z
review text: Let \(G=(V,E)\) be a simple connected graph and \(x\in V(G)\). The set \(\{x^g : g\in Aut(G)\}\) is called an orbit of \(Aut(G)\), the automorphism group of \(G\). This paper determines the edge-connectivity of \(3\)-regular and \(4\)-regular connected graphs with two orbits, and proves the existence of \(k\)-regular \(m\)-edge-connected graphs with two orbits for some given integers \(k\) and \(m\). Furthermore, it is proved that the edge-connectivity of a \(k\)-regular connected graph with two orbits and girth at least \(5\) attains its regular degree \(k\).
reviewed by: Jun-Ming Xu
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 5300689
zbMATH Keywords: edge-connectivity
zbMATH Keywords: orbit
zbMATH Keywords: automorphism group
zbMATH Keywords: regular graph
MaRDI profile type: Publication
full work available at URL: j.disc.2007.07.040
OpenAlex ID: W2025515756
cites work: Q3880849
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DOI: 10.1016/J.DISC.2007.07.040
description: scientific article; zbMATH DE number 5300689