Topological graph theory
Group action graphs and parallel architectures
SIAM Journal on Computing
Quasi-abelian Cayley graphs and Parsons graphs
European Journal of Combinatorics
On adjacency-transitive graphs
Discrete Mathematics - Special issue on Graph theory
On normal cayley graphs and hom-idempotent graphs
European Journal of Combinatorics
Constructing 4-valent 12 -transitive graphs with a nonsolvable automorphism group
Journal of Combinatorial Theory Series B
Discrete Mathematics - Algebraic and topological methods in graph theory
On quasiabelian Cayley graphs and graphical doubly regular representations
Discrete Mathematics - Algebraic and topological methods in graph theory
Discrete Mathematics - Algebraic and topological methods in graph theory
On quasiabelian Cayley graphs and graphical doubly regular representations
Discrete Mathematics - Algebraic and topological methods in graph theory
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An automorphism σ of a finite simple graph Γ is an adjacency automorphism if for every vertex x ∈ V(Γ), either σx = x or σx is adjacent to x in Γ. An adjacency automorphism fixing no vertices is a shift. A connected graph Γ is strongly adjacency-transitive (respectively, uniquely shift-transitive) if there is, for every pair of adjacent vertices x, y ∈ V(Γ), an adjacency automorphism (respectively, a unique shift) σ ∈ Aut Γ sending x to y. The action graph Γ = ActGrph(G,X,S) of a group G acting on a set X, relative to an inverse-closed nonempty subset S ⊆ G, is defined as follows: the vertex-set of Γ is X, and two different vertices x,y ∈ V(Γ) are adjacent in Γ if and only if y=sx for some s ∈ S. A characterization of strongly adjacency-transitive graphs in terms of action graphs is given. A necessary and sufficient condition for cartesian products of graphs to be uniquely shift-transitive is proposed, and two questions concerning uniquely shift-transitive graphs are raised.