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.