On weakly symmetric graphs of order twice a prime
Journal of Combinatorial Theory Series B
A classification of symmetric graphs of order 3p
Journal of Combinatorial Theory Series B
Symmetric graphs of order a product of two distinct primes
Journal of Combinatorial Theory Series B
1/2-Transitive Graphs of Order 3p
Journal of Algebraic Combinatorics: An International Journal
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Automorphism groups and isomorphisms of Cayley digraphs
Discrete Mathematics - Special issue on Graph theory
The solution of a problem of Godsil on cubic Cayley graphs
Journal of Combinatorial Theory Series B
On half-transitive metacirculant graphs of prime-power order
Journal of Combinatorial Theory Series B
Transitive Permutation Groups of Prime-Squared Degree
Journal of Algebraic Combinatorics: An International Journal
On cubic Cayley graphs of finite simple groups
Discrete Mathematics - Algebraic and topological methods in graph theory
A tetravalent half-arc-transitive graph with non-abelian vertex stabilizer
Journal of Combinatorial Theory Series B
On edge-transitive Cayley graphs of valency four
European Journal of Combinatorics
Non-normal one-regular and 4-valent Cayley graphs of dihedral groups D2n
European Journal of Combinatorics
Tetravalent half-arc-transitive graphs of order p4
European Journal of Combinatorics
A classification of tightly attached half-arc-transitive graphs of valency 4
Journal of Combinatorial Theory Series B
Hexavalent half-arc-transitive graphs of order 4p
European Journal of Combinatorics
An infinite family of half-arc-transitive graphs with universal reachability relation
European Journal of Combinatorics
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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 also have arbitrarily large stabilizers. A Cayley graph Cay(G, S) on a group G is said to be normal if the right regular representation R(G) of G is normal in Aut(Cay(G, S)). There are only a few known examples of connected tetravalent non-normal Cayley graphs on non-abelian simple groups. In this article, we give a sufficient condition for non-normal Cayley graphs and by using the condition, infinitely many connected tetravalent non-normal Cayley graphs are constructed. As an application, all connected tetravalent non-normal Cayley graphs on the alternating group A6 are determined. © 2011 Wiley Periodicals, Inc. J Graph Theory © 2012 Wiley Periodicals, Inc.