Eternal total domination in graphs
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. We study some variations of this concept in which the configuration of guards induce total dominating sets. We consider two models of the problem: one in which only one guard moves at a time and one in which all guards may move simultaneously. A number of upper and lower bounds are given for the number of guards required.
Klostermeyer, W.F. & Mynhardt, C.M. (2012) Eternal total domination in graphs. Ars Combinatoria, 107, 473-492.