Characterization of edge-transitive 4-valent bicirculants

István Kovács, Boštjan Kuzman, Aleksander Malnič, Stephen E Wilson

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

A bicirculant is a graph admitting an automorphism with exactly two vertex-orbits of equal size. All non-isomorphic 4-valent edge-transitive bicirculants are characterized in this article. As a corollary, a characterization of 4-valent arc-transitive dihedrants is obtained.

Original languageEnglish (US)
Pages (from-to)441-463
Number of pages23
JournalJournal of Graph Theory
Volume69
Issue number4
DOIs
StatePublished - Apr 2012

Fingerprint

Automorphism
Corollary
Arc of a curve
Orbit
Graph in graph theory
Vertex of a graph

Keywords

  • automorphism group
  • bicirculant graph
  • Cayley graph
  • dihedrant
  • edge-transitive graph
  • rose window graph
  • tetravalent graph

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Characterization of edge-transitive 4-valent bicirculants. / Kovács, István; Kuzman, Boštjan; Malnič, Aleksander; Wilson, Stephen E.

In: Journal of Graph Theory, Vol. 69, No. 4, 04.2012, p. 441-463.

Research output: Contribution to journalArticle

Kovács, István ; Kuzman, Boštjan ; Malnič, Aleksander ; Wilson, Stephen E. / Characterization of edge-transitive 4-valent bicirculants. In: Journal of Graph Theory. 2012 ; Vol. 69, No. 4. pp. 441-463.
@article{f749f239cc8d4bfaa6db6046363d7e64,
title = "Characterization of edge-transitive 4-valent bicirculants",
abstract = "A bicirculant is a graph admitting an automorphism with exactly two vertex-orbits of equal size. All non-isomorphic 4-valent edge-transitive bicirculants are characterized in this article. As a corollary, a characterization of 4-valent arc-transitive dihedrants is obtained.",
keywords = "automorphism group, bicirculant graph, Cayley graph, dihedrant, edge-transitive graph, rose window graph, tetravalent graph",
author = "Istv{\'a}n Kov{\'a}cs and Boštjan Kuzman and Aleksander Malnič and Wilson, {Stephen E}",
year = "2012",
month = "4",
doi = "10.1002/jgt.20594",
language = "English (US)",
volume = "69",
pages = "441--463",
journal = "Journal of Graph Theory",
issn = "0364-9024",
publisher = "Wiley-Liss Inc.",
number = "4",

}

TY - JOUR

T1 - Characterization of edge-transitive 4-valent bicirculants

AU - Kovács, István

AU - Kuzman, Boštjan

AU - Malnič, Aleksander

AU - Wilson, Stephen E

PY - 2012/4

Y1 - 2012/4

N2 - A bicirculant is a graph admitting an automorphism with exactly two vertex-orbits of equal size. All non-isomorphic 4-valent edge-transitive bicirculants are characterized in this article. As a corollary, a characterization of 4-valent arc-transitive dihedrants is obtained.

AB - A bicirculant is a graph admitting an automorphism with exactly two vertex-orbits of equal size. All non-isomorphic 4-valent edge-transitive bicirculants are characterized in this article. As a corollary, a characterization of 4-valent arc-transitive dihedrants is obtained.

KW - automorphism group

KW - bicirculant graph

KW - Cayley graph

KW - dihedrant

KW - edge-transitive graph

KW - rose window graph

KW - tetravalent graph

UR - http://www.scopus.com/inward/record.url?scp=84859810305&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859810305&partnerID=8YFLogxK

U2 - 10.1002/jgt.20594

DO - 10.1002/jgt.20594

M3 - Article

AN - SCOPUS:84859810305

VL - 69

SP - 441

EP - 463

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 4

ER -