A set of vertices S is a determining set for a graph G if every automorphism of G is uniquely determined by its action on S. The determining number of a graph is the size of a sma...
Abstract. It is shown that for graph groups (right-angled Artin groups) the conjugacy problem as well as a restricted version of the simultaneous conjugacy problem can be solved in...
A labeling of a graph G is distinguishing if it is only preserved by the trivial automorphism of G. The distinguishing chromatic number of G is the smallest integer k such that G ...
Let Γ be a finite digraph and let G be a subgroup of the automorphism group of Γ. A directed cycle C of Γ is called G-consistent whenever there is an element of G whose restri...