One-regular graphs of square-free order of prime valency
نویسندگان
چکیده
منابع مشابه
Symmetric graphs of order 4p of valency prime
A graph is symmetric or arc-transitive if its automorphism group acts transitively on vertices, edges and arcs. Let p, q be odd primes with p, q ≥ 5 and X a q-valent symmetric graph of order 4p. In this paper, we proved that X K4p with 4p-1=q, X K2p,2p-2pK2 with 2p-1=q, the quotient graph of X is isomorphic to Kp,p and p=q, or K2p and 2p-1=q.
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A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this article a complete classification of tetravalent one-regular graphs of order twice a product of two primes is given. It follows from this classification that with the exception of four graphs of orders 12 and 30, all such graphs are Cayley graphs on Abelian, dihedral, or generalized dihedral groups.
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In a non-complete graph $Gamma$, a vertex triple $(u,v,w)$ with $v$ adjacent to both $u$ and $w$ is called a $2$-geodesic if $uneq w$ and $u,w$ are not adjacent. The graph $Gamma$ is said to be $2$-geodesic transitive if its automorphism group is transitive on arcs, and also on 2-geodesics. We first produce a reduction theorem for the family of $2$-geodesic transitive graphs of prime power or...
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A subgroup G of automorphisms of a graph X is said to be 1 2-transitive if it is vertex and edge but not arc-transitive. The graph X is said to be 1 2-transitive if Aut X is 1 2-transitive. The graph X is called one-regular if Aut X acts regularly on the set arcs of X. The interplay of three diierent concepts of maps, one-regular graphs and 1 2-transitive group actions on graphs of valency 4 is...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2011
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2010.10.002