\(s\)-regular cyclic coverings of the three-dimensional hypercube \(Q_{3}\).
type: Item
instance of: scholarly article
title: \(s\)-regular cyclic coverings of the three-dimensional hypercube \(Q_{3}\).
zbMATH Open document ID: 1035.05048
DOI: 10.1016/S0195-6698(03)00055-6
author: Kaishun Wang
author: Yan-Quan Feng
published in: European Journal of Combinatorics
publication date: 2003-08-25T00:00:00Z
review text: An \(s\)-regular graph is a graph with an automorphism group acting regularly on the set of \(s\)-arcs. The main result of the paper is the following theorem: Let \(\widetilde X\) be a connected cyclic covering of the 3-dimensional hypercube \(Q_3\) and let the group of fibre-preserving automorphisms of \(\widetilde X\) act arc-transitively. Then, \(\widetilde X\) is either 1-regular or 2-regular. Furthermore the isomorphism classes of all 1-regular and 2-regular graphs \(\widetilde X\) are listed.
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 1970588
reviewed by: Ulrike Baumann
MaRDI profile type: Publication
cites work: Q4306490
cites work: Q4838445
cites work: On weakly symmetric graphs of order twice a prime
cites work: Q4532739
cites work: Remarks on path-transitivity in finite graphs
cites work: Automorphisms of graphs and coverings
cites work: Regular groups of automorphisms of cubic graphs
cites work: On \(2\)-arc-transitive covers of complete graphs
cites work: Constructing an infinite family of cubic 1-regular graphs
cites work: A One-Regular Graph of Degree Three
cites work: Generating all graph coverings by permutation voltage assignments
cites work: Regular graph coverings whose covering transformation groups have the isomorphism extension property
cites work: Vertex-transitive graphs: Symmetric graphs of prime valency
cites work: Group actions, coverings and lifts of automorphisms
cites work: Elementary abelian covers of graphs
cites work: Constructing infinite one-regular graphs
cites work: Lifting graph automorphisms by voltage assignments
cites work: A family of one-regular graphs of valency 4
cites work: Maps and half-transitive graphs of valency 4
cites work: A �-transitive graph of valency 4 with a nonsolvable group of automorphisms
cites work: The trivalent symmetric graphs of girth at most six
cites work: Regular maps from voltage assignments and exponent groups
cites work: Automorphism groups of covering graphs
cites work: Q4484778
cites work: Coverings of graphs and maps, orthogonality, and eigenvectors
cites work: Q5785712
cites work: On the Symmetry of Cubic Graphs
cites work: The smallest nontoroidal chiral maps
description: scientific article; zbMATH DE number 1970588