- Tytuł:
- How Long Can One Bluff in the Domination Game?
- Autorzy:
-
Brešar, Boštan
Dorbec, Paul
Klavžar, Sandi
Košmrlj, Gašpar - Powiązania:
- https://bibliotekanauki.pl/articles/31341979.pdf
- Data publikacji:
- 2017-05-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
domination game
game domination number
bluff graphs
minus graphs
generalized Petersen graphs
Kneser graphs
Cartesian product of graphs
Hamming graphs - Opis:
- 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.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2017, 37, 2; 337-352
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł