- Tytuł:
- Domination Game Critical Graphs
- Autorzy:
-
Bujtás, Csilla
Klavžar, Sandi
Košmrlj, Gašper - Powiązania:
- https://bibliotekanauki.pl/articles/31234048.pdf
- Data publikacji:
- 2015-11-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
domination number
domination game
domination game critical graphs
powers of cycles
trees - Opis:
- The domination game is played on a graph $G$ by two players who alternately take turns by choosing a vertex such that in each turn at least one previously undominated vertex is dominated. The game is over when each vertex becomes dominated. One of the players, namely Dominator, wants to finish the game as soon as possible, while the other one wants to delay the end. The number of turns when Dominator starts the game on $G$ and both players play optimally is the graph invariant $ \gamma_g (G) $, named the game domination number. Here we study the $ \gamma_g$-critical graphs which are critical with respect to vertex predomination. Besides proving some general properties, we characterize $ \gamma_g$-critical graphs with $ \gamma_g = 2$ and with $ \gamma_g = 3$, moreover for each n we identify the (infinite) class of all $\gamma_g$-critical ones among the $n$th powers $ C_N^n$ of cycles. Along the way we determine $\gamma_{g} ( C_N^n ) $ for all $n$ and $N$. Results of a computer search for $ \gamma_g$-critical trees are presented and several problems and research directions are also listed.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2015, 35, 4; 781-796
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł