Pakanun Dokyeesun: Maker-Breaker domination game on Cartesian products of graphs

Abstract. The Maker-Breaker domination game is played on a graph G by two players, called Dominator and Staller. They alternately select an unplayed vertex in G. Dominator wins the game if he forms a dominating set while Staller wins the game if she claims all vertices from a closed neighborhood of a vertex in the graph.  Recently, Forcan and Qi studied the Maker-Baker domination game on Cartesian products of graphs. It was shown that if Dominator wins the D-game and S-game on G, then Dominator also wins the game on the Cartesian product of G and H for any arbitrary H. In our work, we will show who is the winner of the game on the product of paths, stars, and complete bipartite graphs and how fast he/she wins.