论文标题
直径2图上玩的统治游戏
The domination game played on diameter 2 graphs
论文作者
论文摘要
令$γ_g（g）$为图$ g $的游戏主导号码。事实证明，如果$ {\ rm diam}（g）= 2 $，则$γ_g（g）\ le \ left \ lest \ lceil \ frac {n（g）} {2} {2} \ right \ rceil- \ rceil- \ left \ left \ left \ left \ lfloor \ frac \ frac {n（g）} n（n（g）} n（n（g）} 11}}}}} {11}}} {11}} {达到了限制：如果$ {\ rm diam}（g）= 2 $和$ n（g）\ le 10 $，则$γ_g（g）= \ left \ lew \ lceil \ frac {n（g）} {n（g）} {2} {2} {2} {2} \ right \ right \ rceil $，并且只有$ g $是$ g $ g pet $ n pet $ n（或$ n（$ n（确切的十个直径图$ 2 $和订购$ 11 $的订购$ 11 $。
Let $γ_g(G)$ be the game domination number of a graph $G$. It is proved that if ${\rm diam}(G) = 2$, then $γ_g(G) \le \left\lceil \frac{n(G)}{2} \right\rceil- \left\lfloor \frac{n(G)}{11}\right\rfloor$. The bound is attained: if ${\rm diam}(G) = 2$ and $n(G) \le 10$, then $γ_g(G) = \left\lceil \frac{n(G)}{2} \right\rceil$ if and only if $G$ is one of seven sporadic graphs with $n(G)\le 6$ or the Petersen graph, and there are exactly ten graphs of diameter $2$ and order $11$ that attain the bound.
