Semiregular automorphisms of vertex-transitive cubic graphs

Peter Cameron; John Sheehan; Pablo Spiga

doi:10.1016/j.ejc.2005.04.008

Semiregular automorphisms of vertex-transitive cubic graphs

Peter Cameron^*, John Sheehan, Pablo Spiga

^*Corresponding author for this work

Centre for Interdisciplinary Research in Computational Algebra

Research output: Contribution to journal › Article › peer-review

Abstract

An old conjecture of Marušič, Jordan and Klin asserts that any finite vertex-transitive graph has a non-trivial semiregular automorphism. Marušič and Scapellato proved this for cubic graphs. For these graphs, we make a stronger conjecture, to the effect that there is a semiregular automorphism of order tending to infinity with n. We prove that there is one of order greater than 2.

Original language	English
Pages (from-to)	924-930
Number of pages	7
Journal	European Journal of Combinatorics
Volume	27
Issue number	6
DOIs	https://doi.org/10.1016/j.ejc.2005.04.008
Publication status	Published - 1 Aug 2006

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title = "Semiregular automorphisms of vertex-transitive cubic graphs",

abstract = "An old conjecture of Maru{\v s}i{\v c}, Jordan and Klin asserts that any finite vertex-transitive graph has a non-trivial semiregular automorphism. Maru{\v s}i{\v c} and Scapellato proved this for cubic graphs. For these graphs, we make a stronger conjecture, to the effect that there is a semiregular automorphism of order tending to infinity with n. We prove that there is one of order greater than 2.",

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AU - Sheehan, John

AU - Spiga, Pablo

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N2 - An old conjecture of Marušič, Jordan and Klin asserts that any finite vertex-transitive graph has a non-trivial semiregular automorphism. Marušič and Scapellato proved this for cubic graphs. For these graphs, we make a stronger conjecture, to the effect that there is a semiregular automorphism of order tending to infinity with n. We prove that there is one of order greater than 2.

AB - An old conjecture of Marušič, Jordan and Klin asserts that any finite vertex-transitive graph has a non-trivial semiregular automorphism. Marušič and Scapellato proved this for cubic graphs. For these graphs, we make a stronger conjecture, to the effect that there is a semiregular automorphism of order tending to infinity with n. We prove that there is one of order greater than 2.

UR - https://www.scopus.com/pages/publications/33646108346

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DO - 10.1016/j.ejc.2005.04.008

M3 - Article

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SP - 924

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JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

IS - 6

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Semiregular automorphisms of vertex-transitive cubic graphs

Abstract

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