Semiregular automorphisms of vertex-transitive graphs of certain valencies
نویسندگان
چکیده
منابع مشابه
Semiregular Automorphisms of Cubic Vertex Transitive Graphs
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.
متن کاملPermutation Groups, Vertex-transitive Digraphs and Semiregular Automorphisms
A nonidentity element of a permutation group is said to be semiregular if all of its orbits have the same length. The work in this paper is linked to [6] where the problem of existence of semiregular automorphisms in vertex-transitive digraphs was posed. It was observed there that every vertex-transitive digraph of order pk or mp, where p is a prime, k 1 and m p are positive integers, has a sem...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2007
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2006.06.004