2019/02/06 by Vesna Iršič, Iršič, Vesna
Computer Science · #05C57 #05C69 #05C76 #Advanced Graph Theory Research #Artificial Intelligence in Games #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.1902.02087
openalex publication_date 2019/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The connected domination game was recently introduced by Borowiecki,\nFiedorowicz and Sidorowicz as another variation of the domination game. The\nrules are essentially the same, except that the set of played vertices must be\nconnected at all stages of the game. We answer a problem from their paper\nregarding the relation between the number of moves in a game where\nDominator/Staller starts the game. In this paper we also study the relation to\nthe diameter and present graphs with small connected game domination number. We\ndetermine the values on the lexicographic product graphs, and consider the\neffect of predomination of a vertex on the connected game domination number.\n