发表机构
Universidad de Córdoba; Universidad Autónoma de Guerrero（科尔多瓦大学; 格雷罗自治大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对连通图的细分、中间和中心三种图算子，给出了（独立）半全控制数的闭式公式。
AI 中文摘要
一个非平凡连通图$G$的控制集$D$被称为$G$的半全控制集，如果$D$中每个顶点到$D$中另一个顶点的距离至多为2。此外，如果$D$还是独立集，则$D$被称为$G$的独立半全控制集。$G$的（独立）半全控制数是$G$的所有（独立）半全控制集中的最小基数。在本文中，我们针对由连通图定义的三个著名图算子：细分图、中间图和中心图，获得了这些参数的闭式公式。
英文摘要
A dominating set $D$ of a nontrivial connected graph $G$ is called a semitotal dominating set of $G$ if every vertex in $D$ is at distance at most two from another vertex in $D$. If, in addition, $D$ is an independent set, then $D$ is called an independent semitotal dominating set of $G$. The (independent) semitotal domination number of $G$ is the minimum cardinality among all (independent) semitotal dominating sets of $G$. In this paper, we obtain closed formulas for these parameters in the following three well-known graph operators defined from a connected graph: the subdivision, middle, and central graphs.
