Strong domination number of graphs from primary subgraphs
| Autor: | Alikhani, Saeid, Ghanbari, Nima, Henning, Michael A. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 20 pages, 13 figures |
| Databáze: | arXiv |
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