Game domination numbers of a disjoint union of paths and cycles

Abstract

The domination game is played on a graph G by two players, Dominator and Staller, who alternately chooses a vertex of G in such a way that at least one new vertex is dominated. The game ends when all vertices are dominated. Dominator aims to finish the game in as few moves as possible while Staller aims to finish the game in as many moves as possible. The game domination number γ_g (G) (respectively γʹ_g (G)) is the total number of moves both players use in a game which Dominator (respectively Staller) starts and both players use optimal strategies. In this paper we determine the game domination numbers of a disjoint union of paths and cycles.