A dynamic domination problem in trees

Abstract

We consider a dynamic domination problem for graphs in which an infinite sequence of attacks occur at vertices with guards and the guard at the attacked vertex is required to vacate the vertex by moving to a neighboring vertex with no guard. Other guards are allowed to move at the same time, and before and after each attack and the resulting guard movements, the vertices containing guards form a dominating set of the graph. The minimum number of guards that can successfully defend the graph against such an arbitrary sequence of attacks is the m-eviction number. This parameter lies between the domination and independence numbers of the graph. We characterize the classes of trees for which the m-eviction number equals the domination number and the independence number, respectively.

Keywords

• graph protection
• eternal domination
• domination number
• independence number