Semiregular Automorphisms of Cubic Vertex-Transitive Graphs and the Abelian Normal Quotient Method
نویسندگان
چکیده
منابع مشابه
Semiregular Automorphisms of Cubic Vertex-Transitive Graphs and the Abelian Normal Quotient Method
We characterise connected cubic graphs admitting a vertex-transitive group of automorphisms with an abelian normal subgroup that is not semiregular. We illustrate the utility of this result by using it to prove that the order of a semiregular subgroup of maximum order in a vertex-transitive group of automorphisms of a connected cubic graph grows with the order of the graph. ∗This work was suppo...
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It is shown that for a connected cubic graph Γ , a vertex transitive group G ≤ AutΓ contains a large semiregular subgroup. This confirms a conjecture of Cameron and Sheehan (2001).
متن کاملSemiregular Automorphisms of Cubic Vertex-transitive Graphs
We characterise connected cubic graphs admitting a vertextransitive group of automorphisms with an abelian normal subgroup that is not semiregular. We illustrate the utility of this result by using it to prove that the order of a semiregular subgroup of maximum order in a vertex-transitive group of automorphisms of a connected cubic graph grows with the order of the graph, settling [2, Problem ...
متن کاملSemiregular automorphisms of vertex-transitive cubic graphs
An old conjecture of Marušič, Jordan and Klin asserts that any finite vertextransitive 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.
متن کاملSemiregular automorphisms of edge-transitive graphs
The polycirculant conjecture asserts that every vertex-transitive digraph has a semiregular automorphism, that is, a nontrivial automorphism whose cycles all have the same length. In this paper we investigate the existence of semiregular automorphisms of edge-transitive graphs. In particular, we show that any regular edge-transitive graph of valency three or four has a semiregular automorphism.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2015
ISSN: 1077-8926
DOI: 10.37236/4842