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

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7 Citations (Scopus)

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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

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

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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.",

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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

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JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

ER -

Cubic arc-transitive k-multicirculants

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