Abstract:The distinguishing number of a graph was introduced by Albertson and Collins in [1] as a measure of the amount of symmetry contained in the graph. Tymoczko extended this definition to faithful group actions on sets in [11]; taking the set to be the vertex set of a graph and the group to be the automorphism group of the graph allows one to recover the previous definition. Since then, several authors have studied properties of the distinguishing number as well as extensions of the notion. In this paper, we first… Show more
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