Abstract
Eternal domination of a graph requires the vertices of the graph to be protected, against infinitely long sequences of attacks, by guards located at vertices, with the requirement that the configuration of guards induces a dominating set at all times. Klostermeyer and Mynhardt studied some variations of this concept in which the configuration of guards induces total dominating sets (TDSs). They considered two models of the problem, one in which only one guard moves at a time and one in which more than one guard may move simultaneously. In this paper, we consider the model in which all guards move simultaneously when the configuration of guards induces TDSs and we study this model for some classes of graphs.
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