On weakly symmetric graphs of order twice a prime
Journal of Combinatorial Theory Series B
A characterization of a class of symmetric graphs of twice prime valency
European Journal of Combinatorics
Characterizing vertex-transitive pq-graphs with an imprimitive automorphism subgroup
Journal of Graph Theory
Non-Cayley Vertex-Transitive Graphs of Order Twice the Product of Two Odd Primes
Journal of Algebraic Combinatorics: An International Journal
Vertex-transitive graphs that are not Cayley graphs. II
Journal of Graph Theory
Non-Cayley tetravalent metacirculant graphs and their hamiltonicity
Journal of Graph Theory
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
Half-transitivity of some metacirculants
Discrete Mathematics
Group actions, coverings and lifts of automorphisms
Discrete Mathematics - Special issue on Graph theory
On vertex-transitive, non-Cayley graphs of order pqr
Discrete Mathematics - Special issue on Graph theory
Lifting graph automorphisms by voltage assignments
European Journal of Combinatorics
On vertex-transitive graphs of odd prime-power order
Discrete Mathematics
Elementary Abelian Covers of Graphs
Journal of Algebraic Combinatorics: An International Journal
Square-Free Non-Cayley Numbers. On Vertex-Transitive Non-Cayley Graphs of Square-Free Order
Designs, Codes and Cryptography
Invariant subspaces, duality, and covers of the Petersen graph
European Journal of Combinatorics
Tetravalent half-transitive graphs of order 4p
European Journal of Combinatorics
Cubic symmetric graphs of order a small number times a prime or a prime square
Journal of Combinatorial Theory Series B
Cubic vertex-transitive graphs of order 2pq
Journal of Graph Theory
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A graph is vertex-transitive if its automorphism group acts transitively on vertices of the graph. A vertex-transitive graph is a Cayley graph if its automorphism group contains a subgroup acting regularly on its vertices. In this article, the tetravalent vertex-transitive non-Cayley graphs of order 4p are classified for each prime p. As a result, there are one sporadic and five infinite families of such graphs, of which the sporadic one has order 20, and one infinite family exists for every prime p3, two families exist if and only if p≡1 (mod 8) and the other two families exist if and only if p≡1 (mod 4). For each family there is a unique graph for a given order. © 2011 Wiley Periodicals, Inc. (Contract grant sponsor: National Natural Science Foundation of China; Contract grant number: 10901015; Contract grant sponsor: Fundamental Research Funds for the Central Universities; Contract grant numbers: 2011JBM127 and 2011JBZ012; Contract grant sponsor: Science and Technology Foundation of Beijing Jiaotong University; Contract grant number: 2008RC037.)