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Game total domination

Abstract: Let G = (V, E) be a simple graph without isolated vertices. The total domination game, played on a graph G consists of two players called Dominator and Staller who take turns choosing a vertex from G. Each chosen vertex must totally dominate at least one vertex not totally dominated by the set of vertices previously chosen. The game ends when the set of vertices chosen is a total dominating set in G. Dominator’s objective is to minimize the number of vertices chosen, while Staller’s is to end the game with as many vertices chosen as possible. The game total domination number, \$\gama_{tg}(G)\$ is the number of vertices chosen when Dominator starts the game and both players employ a strategy that achievestheir objective. The Staller-start game total domination number, \$\gama'_{tg}(G)\$ is the number of vertices chosen when Staller starts the game and both players play optimally. In this talk, some results about \$\gama_{tg}(G)\$ and \$\gama'_{tg}(G)\$ will be given.