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How Long Can One Bluff in the Domination Game?

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Brešar B., Dorbec P., Klavžar S., Košmrlj G.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 2

337-352

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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Brešar B.

1 Dorbec P.

1 Klavžar S.

1 Košmrlj G.

1 2017

Wyniki wyszukiwania

How Long Can One Bluff in the Domination Game?