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Tetravalent half-edge-transitive graphs and non-normal Cayley graphs

✍ Scribed by Xiuyun Wang; Yan-Quan Feng

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
206 KB
Volume
70
Category
Article
ISSN
0364-9024

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✦ Synopsis

Let X be a vertex-transitive graph, that is, the automorphism group Aut(X ) of X is transitive on the vertex set of X . The graph X is said to be symmetric if Aut(X ) is transitive on the arc set of X . Suppose that Aut(X ) has two orbits of the same length on the arc set of X . Then X is said to be half-arc-transitive or half-edge-transitive if Aut(X ) has one or two orbits on the edge set of X , respectively. Stabilizers of symmetric and half-arc-transitive graphs have been investigated by many authors. For example, see Tutte [Canad J Math 11 (1959), 621-624] and Conder and Marušič [J Combin Theory Ser B 88 (2003), 67-76]. It is trivial to construct connected tetravalent symmetric graphs with arbitrarily large stabilizers, and by Marušič [Discrete Math 299 (2005), 180-193], connected tetravalent half-arc-transitive graphs can have arbitrarily large stabilizers. In this article, we show that connected tetravalent half-edge-transitive graphs can

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