论文标题
图II的超级统治数的一些结果
Some results on the super domination number of a graph II
论文作者
论文摘要
令$ g =（v，e）$为一个简单的图。 $ g $的主导集是一个子集$ s \ subseteq v $，因此每个顶点$ s $中的每个顶点至少与$ s $中的至少一个顶点相邻。由$γ（g）$表示的最小统治$ g $的基数是$ g $的统治数。如果每个顶点$ u \ in \ In \ overline {s} = v-s $，则称为$ g $的超级统治集$ s $，在s $中存在$ v \，以至于$ n（v）\ cap \ cap \ overline {s} = \ {u \ \ \ \} $。 $γ_{sp}（g）$表示的最小超级主导套件的基数是$ g $的超级统治数。在本文中，我们获得了图形的超级支配数量的更多结果，该图由顶点上的操作修改。另外，我们为成对分离图的链和花束的超级统治数量提供了一些锋利的边界。
Let $G=(V,E)$ be a simple graph. A dominating set of $G$ is a subset $S\subseteq V$ such that every vertex not in $S$ is adjacent to at least one vertex in $S$. The cardinality of a smallest dominating set of $G$, denoted by $γ(G)$, is the domination number of $G$. A dominating set $S$ is called a super dominating set of $G$, if for every vertex $u\in \overline{S}=V-S$, there exists $v\in S$ such that $N(v)\cap \overline{S}=\{u\}$. The cardinality of a smallest super dominating set of $G$, denoted by $γ_{sp}(G)$, is the super domination number of $G$. In this paper, we obtain more results on the super domination number of graphs which is modified by an operation on vertices. Also, we present some sharp bounds for super domination number of chain and bouquet of pairwise disjoint connected graphs.
