论文标题
图形的超级统治数的一些结果
Some results on the super domination number of a graph
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，我们研究了某些图类别的超级统治数，并为某些图形操作提供了尖锐的边界。
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 study super domination number of some graph classes and present sharp bounds for some graph operations.
