Tetravalent one-regular graphs of order 2pq

Authors:
Jin-Xin Zhou;Yan-Quan Feng
Affiliations:
Department of Mathematics, Beijing Jiaotong University, Beijing, China 100044;Department of Mathematics, Beijing Jiaotong University, Beijing, China 100044
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2009

Citing 16
Cited 2

On weakly symmetric graphs of order twice a prime

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A classification of symmetric graphs of order 3p

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Symmetric graphs of order a product of two distinct primes

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Vertex-primitive graphs of order a product of two distinct primes

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On 4-valent symmetric graphs

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A characterization of certain families of 4-valent symmetric graphs

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Remarks on path-transitivity in finite graphs

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A family of one-regular graphs of valency 4

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The MAGMA algebra system I: the user language

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Constructing infinite one-regular graphs

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Classifying cubic symmetric graphs of order 8p or 8p2

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Non-normal one-regular and 4-valent Cayley graphs of dihedral groups D2n

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Cubic symmetric graphs of order a small number times a prime or a prime square

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One-regular graphs of square-free order of prime valency

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Arc-regular cubic graphs of order four times an odd integer

Journal of Algebraic Combinatorics: An International Journal

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Abstract

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.