Title: Strong domination number of graphs from primary subgraphs Show Chinese title

Title: 从初级子图中得到的图的强支配数

Abstract: A set $D$ of vertices is a strong dominating set in a graph $G$, if for every vertex $x\in V(G) \setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $deg(x) \leq deg(y)$. The strong domination number $\gamma_{st}(G)$ of $G$ is the minimum cardinality of a strong dominating set in $G$. Let $G$ be a connected graph constructed from pairwise disjoint connected graphs $G_1,\ldots ,G_k$ by selecting a vertex of $G_1$, a vertex of $G_2$, and identifying these two vertices, and thereafter continuing in this manner inductively. The graphs $G_1,\ldots ,G_k$ are the primary subgraphs of $G$. In this paper, we study the strong domination number of $K_r$-gluing of two graphs and investigate the strong domination number for some particular cases of graphs from their primary subgraphs. Show Chinese abstract

Abstract: 一个顶点集$D$是图$G$中的强支配集，如果对于每个顶点$x\in V(G) \setminus D$都存在一个顶点$y\in D$使得$xy\in E(G)$并且$deg(x) \leq deg(y)$。 强支配数$\gamma_{st}(G)$的$G$是$G$中强支配集的最小基数。 设$G$是一个由两两不相交的连通图$G_1,\ldots ,G_k$构造而成的连通图，方法是选择$G_1$中的一个顶点，$G_2$中的一个顶点，并将这两个顶点进行标识，然后以这种方式继续递归地进行。 图$G_1,\ldots ,G_k$是图$G$的主要子图。 在本文中，我们研究两个图的$K_r$粘合的强支配数，并探讨从其主要子图中的一些特定情况的强支配数。