Constructing infinite one-regular graphs
type: Item
instance of: scholarly article
title: Constructing infinite one-regular graphs
zbMATH Open document ID: 0943.05044
author: Aleksander Malnič
author: Dragan Marušič
author: Norbert Seifter
published in: European Journal of Combinatorics
publication date: 2000-09-05T00:00:00Z
review text: A graph \(X\) is said to be one-regular if the automorphism group of \(X\) acts regularly on the set of arcs of \(X\). The authors consider infinite one-regular graphs. Starting with an infinite family of finite one-regular graphs of valency 4, for each member of this family an infinite one-regular graph is constructed. These graphs are Cayley graphs of almost abelian groups and represent a subclass of graphs with polynomial growth.
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 1417661
zbMATH Keywords: automorphism group
zbMATH Keywords: one-regular graphs
zbMATH Keywords: Cayley graphs
reviewed by: Ulrike Baumann
MaRDI profile type: Publication
full work available at URL: eujc.1999.0338
OpenAlex ID: W2011335266
cites work: Q4306490
cites work: Remarks on path-transitivity in finite graphs
cites work: Automorphisms of graphs and coverings
cites work: A One-Regular Graph of Degree Three
cites work: On 4-valent symmetric graphs
cites work: A characterization of certain families of 4-valent symmetric graphs
cites work: Graphs with polynomial growth are covering graphs
cites work: Q3757929
cites work: A survey on graphs with polynomial growth
cites work: A family of one-regular graphs of valency 4
cites work: The trivalent symmetric graphs of girth at most six
cites work: p-solvable doubly transitive permutation groups
cites work: Properties of graphs with polynomial growth
cites work: Graphs and finite permutation groups
cites work: Graphs and finite permutation groups. II
cites work: AUTOMORPHISMS OF GRAPHS AND A CHARACTERIZATION OF LATTICES
cites work: GRAPHS WITH POLYNOMIAL GROWTH
cites work: Q5785712
cites work: The nonexistence of 8-transitive graphs
cites work: Q5512231
cites work: How to determine the maximum genus of a graph
DOI: 10.1006/EUJC.1999.0338
description: scientific article; zbMATH DE number 1417661