Topological graph theory
Automorphism groups of symmetric graphs of valency 3
Journal of Combinatorial Theory Series B - Series B
Isomorphisms and automorphisms of graph coverings
Discrete Mathematics
Remarks on path-transitivity in finite graphs
European Journal of Combinatorics
Regular embeddings of canonical double coverings of graphs
Journal of Combinatorial Theory Series B
Automorphism groups of covering graphs
Journal of Combinatorial Theory Series B
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
Regular maps from voltage assignments and exponent groups
European Journal of Combinatorics
On 2-arc-transitive covers of complete graphs
Journal of Combinatorial Theory Series B
Lifting graph automorphisms by voltage assignments
European Journal of Combinatorics
On finite s-transitive graphs of odd order
Journal of Combinatorial Theory Series B
On 2-arc-transitivity of Cayley graphs
Journal of Combinatorial Theory Series B
s-Regular cyclic coverings of the three-dimensional hypercube Q3
European Journal of Combinatorics
Elementary Abelian Covers of Graphs
Journal of Algebraic Combinatorics: An International Journal
2-Arc-transitive regular covers of complete graphs Having the covering transformation group Zp3
Journal of Combinatorial Theory Series B
Finite symmetric graphs with two-arc transitive quotients
Journal of Combinatorial Theory Series B
Classifying cubic symmetric graphs of order 8p or 8p2
European Journal of Combinatorics
Journal of Combinatorial Theory Series B
Non-normal one-regular and 4-valent Cayley graphs of dihedral groups D2n
European Journal of Combinatorics
s-Regular cubic graphs as coverings of the complete bipartite graph K3,3
Journal of Graph Theory
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A regular covering projection @?:X@?-X of connected graphs is G-admissible if G lifts along @?. Denote by G@? the lifted group, and let CT(@?) be the group of covering transformations. The projection is called G-split whenever the extension CT(@?)-G@?-G splits. In this paper, split 2-covers are considered, with a particular emphasis given to cubic symmetric graphs. Supposing that G is transitive on X, a G-split cover is said to be G-split-transitive if all complements G@?@?G of CT(@?) within G@? are transitive on X@?; it is said to be G-split-sectional whenever for each complement G@? there exists a G@?-invariant section of @?; and it is called G-split-mixed otherwise. It is shown, when G is an arc-transitive group, split-sectional and split-mixed 2-covers lead to canonical double covers. Split-transitive covers, however, are considerably more difficult to analyze. For cubic symmetric graphs split 2-cover are necessarily canonical double covers (that is, no G-split-transitive 2-covers exist) when G is 1-regular or 4-regular. In all other cases, that is, if G is s-regular, s=2,3 or 5, a necessary and sufficient condition for the existence of a transitive complement G@? is given, and moreover, an infinite family of split-transitive 2-covers based on the alternating groups of the form A"1"2"k"+"1"0 is constructed. Finally, chains of consecutive 2-covers, along which an arc-transitive group G has successive lifts, are also considered. It is proved that in such a chain, at most two projections can be split. Further, it is shown that, in the context of cubic symmetric graphs, if exactly two of them are split, then one is split-transitive and the other one is either split-sectional or split-mixed.