How long can one bluff in the domination game?Brešar, Boštjan (Avtor) Dorbec, Paul (Avtor) Klavžar, Sandi (Avtor) Košmrlj, Gašper (Avtor) domination gamegame domination numberbluff graphsminus graphsgeneralized Petersen graphsKneser graphsCartesian product of graphsHamming graphsThe domination game is played on an arbitrary graph ▫$G$▫ by two players, Dominator and Staller. The game is called Game 1 when Dominator starts it, and Game 2 otherwise. In this paper bluff graphs are introduced as the graphs in which every vertex is an optimal start vertex in Game 1 as well as in Game 2. It is proved that every minus graph (a graph in which Game 2 finishes faster than Game 1) is a bluff graph. A non-trivial infinite family of minus (and hence bluff) graphs is established. Minus graphs with game domination number equal to 3 are characterized. Double bluff graphs are also introduced and it is proved that Kneser graphs ▫$K(n,2)$▫, za ▫$n \ge 6$▫, are double bluff. The domination game is also studied on generalized Petersen graphs and on Hamming graphs. Several generalized Petersen graphs that are bluff graphs but not vertex-transitive are found. It is proved that Hamming graphs are not double bluff.University of Zielona Góra20172017-05-09 15:18:30Znanstveno delo65601ISSN: 1234-3099UDK: 519.17OceCobissID: 7487065COBISS_ID: 17978457DOI: 10.7151/dmgt.1899ISSN pri članku: 1234-3099NUK URN: URN:SI:UM:DK:DMQJPGXSsl