论文标题
其顶点集的图表的存在可以分配到固定数量的统治强度临界顶点集
The Existence of Graph whose Vertex Set Can be Partitioned into a Fixed Number of Domination Strong Critical Vertex-sets
论文作者
论文摘要
令$γ（g）$表示图$ g $的统治数。如果$γ（g-v）=γ（g）-1 $，则V（g）$中的顶点$ v \ $ g $的c {crigint {crigine vertex}。如果每个顶点的每个顶点都是关键的，则将图称为\ emph {vertex-Critical}。在本文中，我们相应地介绍了两个这样的定义：（i）$ s \ subseteq v（g）$称为$ g $的$ g $，如果$γ（g-s）=γ（g） - | s | $; （ii）如果$ v（g）$可以将$ g $ g $称为\ emph {strong $ l $ -vertex-sets-Critical}，则可以将$ v（g）$划分为$ l $ l $ strong critical critical critical tertex sets $ g $。在此之前，我们通过扩展顶点临界图的先前结果来提供一些强$ L $ -VERTEX-SETS-CRIGITATION图的属性。作为核心工作，我们研究了这类图的存在，并在且仅当$ l \ notin \ {2,3,5 \} $时，就存在强大的$ l $ vertex-sets-Contine-Contioncected Graph。
Let $γ(G)$ denote the domination number of a graph $G$. A vertex $v\in V(G)$ is called a \emph{critical vertex} of $G$ if $γ(G-v)=γ(G)-1$. A graph is called \emph{vertex-critical} if every vertex of it is critical. In this paper, we correspondingly introduce two such definitions: (i) a set $S\subseteq V(G)$ is called a \emph{strong critical vertex-set} of $G$ if $γ(G-S)=γ(G)-|S|$; (ii) a graph $G$ is called \emph{strong $l$-vertex-sets-critical} if $V(G)$ can be partitioned into $l$ strong critical vertex-sets of $G$. Whereafter, we give some properties of strong $l$-vertex-sets-critical graphs by extending the previous results of vertex-critical graphs. As the core work, we study on the existence of this class of graphs and obtain that there exists a strong $l$-vertex-sets-critical connected graph if and only if $l\notin\{2,3,5\}$.
