A characterization of metacirculants

Authors:
Cai Heng Li;Shu Jiao Song;Dian Jun Wang
Affiliations:
School of Mathematics and Statistics, Yunnan University, Kunming, Yunnan 650091, PR China and School of Mathematics and Statistics, The University of Western Australia, Crawley 6009 WA, Australia;Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China and Department of Science and Mathematics, Tsinghua University, Beijing 100084, PR China;Department of Science and Mathematics, Tsinghua University, Beijing 100084, PR China
Venue:
Journal of Combinatorial Theory Series A
Year:
2013

Citing 12
Cited 0

Half-Transitive Graphs of Prime-Cube Order

Journal of Algebraic Combinatorics: An International Journal
A Classification of 2-Arc-Transitive Circulants

Journal of Algebraic Combinatorics: An International Journal
Non-Cayley tetravalent metacirculant graphs and their hamiltonicity

Journal of Graph Theory
Half-transitivity of some metacirculants

Discrete Mathematics
Group actions, coverings and lifts of automorphisms

Discrete Mathematics - Special issue on Graph theory
On half-transitive metacirculant graphs of prime-power order

Journal of Combinatorial Theory Series B
On 2-arc-transitivity of Cayley graphs

Journal of Combinatorial Theory Series B
Classifying Arc-Transitive Circulants

Journal of Algebraic Combinatorics: An International Journal
Permutation Groups with a Cyclic Regular Subgroup and Arc Transitive Circulants

Journal of Algebraic Combinatorics: An International Journal
On quartic half-arc-transitive metacirculants

Journal of Algebraic Combinatorics: An International Journal
Classification of 2-arc-transitive dihedrants

Journal of Combinatorial Theory Series B
On dihedrants admitting arc-regular group actions

Journal of Algebraic Combinatorics: An International Journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

Metacirculants were introduced by Alspach and Parsons in 1982 and have been a rich source of various topics since then, including the Hamiltonian path problem in metacirculants. A metacirculant has a vertex-transitive metacyclic subgroup of automorphisms, and a long-standing interesting question in the area is if the converse statement is true, namely, whether a graph with a vertex-transitive metacyclic automorphism group is a metacirculant. We shall answer this question in the negative, and then present a classification of cubic metacirculants.