Topological graph theory
On group graphs and their fault tolerance
IEEE Transactions on Computers
A Group-Theoretic Model for Symmetric Interconnection Networks
IEEE Transactions on Computers
Group action graphs and parallel architectures
SIAM Journal on Computing
Lifting map automorphisms and MacBeath's theorem
Journal of Combinatorial Theory Series B
Isomorphisms and automorphisms of graph coverings
Discrete Mathematics
Which generalized Petersen graphs are Cayley graphs?
Journal of Graph Theory
Graph covering projections arising from finite vector spaces over finite fields
Discrete Mathematics
Automorphism groups of covering graphs
Journal of Combinatorial Theory Series B
Group actions, coverings and lifts of automorphisms
Discrete Mathematics - Special issue on Graph theory
Isomorphism Classes of Concrete Graph Coverings
SIAM Journal on Discrete Mathematics
Constructing 4-valent 12 -transitive graphs with a nonsolvable automorphism group
Journal of Combinatorial Theory Series B
Lifting graph automorphisms by voltage assignments
European Journal of Combinatorics
Strongly adjacency-transitive graphs and uniquely shift-transitive graphs
Discrete Mathematics - Algebraic and topological methods in graph theory
Strongly adjacency-transitive graphs and uniquely shift-transitive graphs
Discrete Mathematics - Algebraic and topological methods in graph theory
Regular homomorphisms and regular maps
European Journal of Combinatorics
Generation of various classes of trivalent graphs
Theoretical Computer Science
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An action graph is a combinatorial representation of a group acting on a set. Comparing two group actions by an epimorphism of actions induces a covering projection of the respective graphs. This simple observation generalizes and unifies many well-known results in graph theory, with applications ranging from the theory of maps on surfaces and group presentations to theoretical computer science, among others. Reconstruction of action graphs from smaller ones is considered, some results on lifting and projecting the equivariant group of automorphisms are proved, and a special case of the split-extension structure of lifted groups is studied. Action digraphs in connection with group presentations are also discussed.