Paired-domination game played on cycles.

In this paper, we continue the study of the domination game on graphs introduced by Brešar et al. (2010). Haynes and Henning in 2009 introduced a paired-domination version of the domination game. We study an alternative paired-domination version of the domination game played on a graph G by two players, named Dominator and Staller. The players take turns choosing a pair of adjacent vertices of G such that neither vertex in the pair has yet been chosen and the vertices in the pair must dominate at least one vertex not dominated by the previously chosen vertices. This process eventually produces a paired-dominating set of vertices of G ; that is, a dominating set in G that induces a subgraph that contains a perfect matching. Dominator wishes to minimize the number of vertices chosen, while Staller wishes to maximize it. The game paired-domination number γ gpr (G) of G is the number of vertices chosen when Dominator starts the game and both players play optimally, and the Staller-start game paired-domination number γ gpr ′ (G) of G is the number of vertices chosen when Staller starts the game and both players play optimally. In this paper, we determine the paired-domination numbers γ gpr (G) and γ gpr ′ (G) when the graph G is a cycle. [ABSTRACT FROM AUTHOR]