论文标题
国王网格中的最佳定位配对套件
Optimal Locating-Paired-Dominating Sets in King Grids
论文作者
论文摘要
在本文中，我们继续研究McCoy和Henning引入的图表中的定位配对式缩写LPD。给定有限或无限图$ g =（v，e）$，如果诱导子图$ g [s] $具有完美的匹配，并且$ v $中的每个顶点与$ s $中的顶点相邻，则配对$ s \ subset v $是配对的。 LPD的另一个条件要求对于任何不同的顶点$ u，v \ in v \ backslash s $，我们有$ n（u）\ cap s \ neq n（v）\ cap s $。受Kinawi，Hussain和Niepel的猜想的激励，我们证明，国王网格中LPD的最小密度在$ 8/37 $和$ 2/9 $之间，我们发现许多不同的LPD在国王网格中具有$ 2/9 $的密度。这些结果部分解决了它们的猜想。
In this paper, we continue the study of locating-paired-dominating set, abbreviated LPDS, in graphs introduced by McCoy and Henning. Given a finite or infinite graph $G=(V,E)$, a set $S\subset V$ is paired-dominating if the induced subgraph $G[S]$ has a perfect matching and every vertex in $V$ is adjacent to a vertex in $S$. The other condition for LPDS requires that for any distinct vertices $u,v \in V\backslash S$, we have $N(u)\cap S\neq N(v)\cap S$. Motivated by the conjecture of Kinawi, Hussain and Niepel, we prove the minimal density of LPDS in the king grid is between $8/37$ and $2/9$, and we find uncountable many different LPDS with density $2/9$ in the king grid. These results partially solve their conjecture.
