Cubic arc-transitive k-multicirculants

Michael Giudici; István Kovács; Cai Heng Li; Gabriel Verret

doi:10.1016/j.jctb.2017.03.001

Cubic arc-transitive k-multicirculants

Michael Giudici, István Kovács, Cai Heng Li, Gabriel Verret

Research output: Contribution to journal › Article

3 Citations (Scopus)

150 Downloads (Pure)

Abstract

For an integer k⩾1, a graph is called a k-multicirculant if its automorphism group contains a cyclic semiregular subgroup with k orbits on the vertices. If k is even, there exist infinitely many cubic arc-transitive k-multicirculants. We conjecture that, if k is odd, then a cubic arc-transitive k-multicirculant has order at most 6k². Our main result is a proof of this conjecture when k is squarefree and coprime to 6.

Original language	English
Pages (from-to)	80-94
Number of pages	15
Journal	Journal of Combinatorial Theory. Series B
Volume	125
DOIs	https://doi.org/10.1016/j.jctb.2017.03.001
Publication status	Published - 1 Jul 2017

Access to Document

10.1016/j.jctb.2017.03.001

PostReferee2(NoColor)Accepted author manuscript, 376 KBLicence: CC BY-NC-ND

Link to publication in Scopus

Fingerprint Dive into the research topics of 'Cubic arc-transitive k-multicirculants'. Together they form a unique fingerprint.

Cite this

@article{0d4e42f1520741b6bfaa72ecba335398,

title = "Cubic arc-transitive k-multicirculants",

abstract = "For an integer k⩾1, a graph is called a k-multicirculant if its automorphism group contains a cyclic semiregular subgroup with k orbits on the vertices. If k is even, there exist infinitely many cubic arc-transitive k-multicirculants. We conjecture that, if k is odd, then a cubic arc-transitive k-multicirculant has order at most 6k2. Our main result is a proof of this conjecture when k is squarefree and coprime to 6.",

keywords = "Arc-transitive, Circulant, Cubic graph",

author = "Michael Giudici and Istv{\'a}n Kov{\'a}cs and Li, {Cai Heng} and Gabriel Verret",

year = "2017",

month = jul,

day = "1",

doi = "10.1016/j.jctb.2017.03.001",

language = "English",

volume = "125",

pages = "80--94",

journal = "Journal of combinatorial Theory Series B",

issn = "0095-8956",

publisher = "Academic Press",

}

TY - JOUR

T1 - Cubic arc-transitive k-multicirculants

AU - Giudici, Michael

AU - Kovács, István

AU - Li, Cai Heng

AU - Verret, Gabriel

PY - 2017/7/1

Y1 - 2017/7/1

N2 - For an integer k⩾1, a graph is called a k-multicirculant if its automorphism group contains a cyclic semiregular subgroup with k orbits on the vertices. If k is even, there exist infinitely many cubic arc-transitive k-multicirculants. We conjecture that, if k is odd, then a cubic arc-transitive k-multicirculant has order at most 6k2. Our main result is a proof of this conjecture when k is squarefree and coprime to 6.

AB - For an integer k⩾1, a graph is called a k-multicirculant if its automorphism group contains a cyclic semiregular subgroup with k orbits on the vertices. If k is even, there exist infinitely many cubic arc-transitive k-multicirculants. We conjecture that, if k is odd, then a cubic arc-transitive k-multicirculant has order at most 6k2. Our main result is a proof of this conjecture when k is squarefree and coprime to 6.

KW - Arc-transitive

KW - Circulant

KW - Cubic graph

UR - http://www.scopus.com/inward/record.url?scp=85015709031&partnerID=8YFLogxK

U2 - 10.1016/j.jctb.2017.03.001

DO - 10.1016/j.jctb.2017.03.001

M3 - Article

AN - SCOPUS:85015709031

VL - 125

SP - 80

EP - 94

JO - Journal of combinatorial Theory Series B

JF - Journal of combinatorial Theory Series B

SN - 0095-8956

ER -