Geodesic
How Long Can One Bluff in the Domination Game?
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 2, pp. 337-352

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The 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), n ≥ 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.
Keywords: domination game, game domination number, bluff graphs, minus graphs, generalized Petersen graphs, Kneser graphs, Cartesian product of graphs, Hamming graphs 
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Brešar, Boštan; Dorbec, Paul; Klavžar, Sandi; Košmrlj, Gašpar. How Long Can One Bluff in the Domination Game?. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 2, pp. 337-352. http://geodesic.mathdoc.fr/item/DMGT_2017_37_2_a2/