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. © 2005 Elsevier Ltd. All rights reserved
Cameron, P., Sheehan, J., Spiga, P. (2006). Semiregular automorphisms of vertex-transitive cubic graphs. EUROPEAN JOURNAL OF COMBINATORICS, 27(6), 924-930 [10.1016/j.ejc.2005.04.008].
Semiregular automorphisms of vertex-transitive cubic graphs
SPIGA, PABLOUltimo
2006
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. © 2005 Elsevier Ltd. All rights reserved
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