Dominating sequences under atomic changes with applications in Sierpiński and interval graphs
Boštjan Brešar, Tanja Gologranc, Tim Kos · Applicable Analysis and Discrete Mathematics · 2016
In this paper we continue the study of the Grundy domination number of a graph. A linear algorithm to determine the Grundy domination number of an interval graph is presented. The exact value of the Grundy domination number of an arbitrary Sierpiński graph is proven, and efficient algorithms to construct the corresponding sequences are presented. These results are obtained by using sharp bounds for the Grundy domination number of a vertex- and edge-removed graph, proven in this paper.