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2017 | 37 | 2 | 337-352
Tytuł artykułu

How Long Can One Bluff in the Domination Game?

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Rocznik
Tom
37
Numer
2
Strony
337-352
Opis fizyczny
Daty
wydano
2017-05-01
otrzymano
2015-10-19
zaakceptowano
2016-01-07
online
2017-04-01
Twórcy
  • Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia Institute of Mathematics, Physics and Mechanics, Ljubljana,, bostjan.bresar@um.si
autor
  • Univ. Bordeaux, LaBRI, UMR 5800, F-33400 Talence, France CNRS, LaBRI, UMR 5800, F-33400 Talence,, paul.dorbec@u-bordeaux.fr
  • Faculty of Mathematics and Physics, University of Ljubljana, Slovenia Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia Institute of Mathematics, Physics and Mechanics, Ljubljana,, sandi.klavzar@fmf.uni-lj.si
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1899
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