A Dynamic Domination Problem. (2nd November 2015) - Klostermeyer, William F.
Abstract: A dynamic domination problem in graphs is studied in which an innite sequence of attacks occurs at vertices with guards and the guard at the attacked vertex is required to vacate the vertex by moving to a neighboring vertex. Other guards are allowed to move at the same time, and before and after each attack, the vertices containing guards must form a dominating set. We are concerned with the minimum number of guards required to achieve this goal against any arbitrary sequence of attacks; this number is called the swap number. The swap number lies between the domination and independence numbers of the graph; bounds for some classes of graphs are examined in this paper.