Domination gamesIršič Chenoweth, Vesna (Avtor) Klavžar, Sandi (Mentor) Bujtás, Csilla (Komentor) domination in graphsdomination gametotal domination gameZ-domination gameconnected domination gameIn the last decade, domination games have received an increasing amount of attention. In the basic version of the game, two players, Dominator and Staller, take turns to dominate vertices of a graph. Dominator aims to minimize the number of moves while Staller aims to maximize the number of moves. If both players play optimally, the number of moves is a graph invariant called the game domination number of the graph. In this thesis, we focus on the domination game and its variations total domination game, Z-domination game, and connected domination game. We discuss Rall's $1/2$-conjecture for the domination game and provide several partial results to support it. We also investigate a general upper bound for the game domination number. We introduce perfect graphs for domination and total domination games, and present their characterizations, along with several other results. For the total domination game we study the effect of predomination and vertex removal. In particular, we resolve the predomination case. Both Z-domination game and connected domination game have been introduced only recently. We compare the length of the Z-domination game with other domination games and focus on equality cases. For the connected domination game we present several new results, including the solution of the game on lexicographic products, several results on Cartesian products, and the relationship between Dominator- and Staller-start game.20212021-09-23 07:15:08Doktorsko delo/naloga131098UDK: 519.17VisID: 120634COBISS_ID: 78390787sl