论文标题
将Grundy的统治扩展到$ K $ -Grundy的统治
Extending Grundy domination to $k$-Grundy domination
论文作者
论文摘要
图$ g =（v，e）$的Grundy支配数是唯一最长的唯一顶点的长度$ s =（v_1，\ ldots，v_k）$满足$ n [v_i] \ setMinus \ setMinus \ cup_ \ cup_ {最近，引入了该概念的概括，称为$ k $ -grundy统治。在$ k $ -grundy的统治中，如果$ s $具有邻居$ u $，则可以将顶点$ v $包含在$ s $中，以便$ u $出现在不到$ s $ s $的$ k $顶点的关闭社区中。在本文中，我们确定了某些图形家庭的$ K $ -Grundy统治号码，找到$ K $ -L $ -L $ -GRUNDY统治号码的基于学位的界限，并定义了$ K $ -Z $ -Z $ -Z $ -GRUNDY统治号码与$ K $的关系之间的关系。
The Grundy domination number of a graph $G = (V,E)$ is the length of the longest sequence of unique vertices $S = (v_1, \ldots, v_k)$ satisfying $N[v_i] \setminus \cup_{j=1}^{i-1}N[v_j] \neq \emptyset$ for each $i \in [k]$. Recently, a generalization of this concept called $k$-Grundy domination was introduced. In $k$-Grundy domination, a vertex $v$ can be included in $S$ if it has a neighbor $u$ such that $u$ appears in the closed neighborhood of fewer than $k$ vertices of $S$. In this paper, we determine the $k$-Grundy domination number for some families of graphs, find degree-based bounds for the $k$-$L$-Grundy domination number, and define a relationship between the $k$-$Z$-Grundy domination number and the $k$-forcing number of a graph.
