Dominating sequences under atomic changes with applications in sierpinski and interval graphs

Abstract

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 Sierpinski 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.