Topological graph theory
A characterization of a class of symmetric graphs of twice prime valency
European Journal of Combinatorics
Automorphism groups and isomorphisms of Cayley digraphs
Discrete Mathematics - Special issue on Graph theory
Classifying Arc-Transitive Circulants
Journal of Algebraic Combinatorics: An International Journal
Permutation Groups with a Cyclic Regular Subgroup and Arc Transitive Circulants
Journal of Algebraic Combinatorics: An International Journal
Tetravalent edge-transitive graphs of girth at most 4
Journal of Combinatorial Theory Series B
Consistent Cycles in Graphs and Digraphs
Graphs and Combinatorics
Journal of Graph Theory
Journal of Graph Theory
A complete classification of cubic symmetric graphs of girth 6
Journal of Combinatorial Theory Series B
Hamiltonian cycles in cubic Cayley graphs: the {2,4k,3} case
Journal of Algebraic Combinatorics: An International Journal
Handbook of Product Graphs, Second Edition
Handbook of Product Graphs, Second Edition
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The topic of this paper is connected tetravalent graphs admitting an arc-transitive group of automorphisms G, such that the vertex-stabiliser G"v is isomorphic to the Klein 4-group. Such a graph will be called locally-Klein. A cycle in a graph is said to be consistent if there exists an automorphism of the graph that preserves the cycle set-wise and acts upon it as a one-step rotation. The main result of the paper is a classification of those locally-Klein graphs that contain a consistent cycle of length more than half the order of the graph. As a side result, we define an interesting family of graphs embedded on the torus or on the Klein bottle, such that the automorphism group of the resulting map has two orbits on the edges, two orbits on the vertices and two orbits on the arcs of the graph.