Mobile guards on the vertices of a graph are used to defend it against an infinite sequence of attacks on its vertices. The locations of the guards must induce a vertex cover at all times. We compare this new model of graph protection with other previously studied parameters, including such as the eternal domination number and the variation of the eternal vertex cover problem in which attacks occur at edges
Citation
William F.Klostermeyer. An Eternal Vertex Cover Problem[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 085. 79-95. .