A Vizing-type result for semi-total domination
| Autor: | Asplund, John, Davila, Randy, Krop, Elliot |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Discrete Applied Mathematics 258: 8-12, (2019) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.dam.2018.11.023 |
| Popis: | A set of vertices $S$ in a simple isolate-free graph $G$ is a semi-total dominating set of $G$ if it is a dominating set of $G$ and every vertex of $S$ is within distance 2 or less with another vertex of $S$. The semi-total domination number of $G$, denoted by $\gamma_{t2}(G)$, is the minimum cardinality of a semi-total dominating set of $G$. In this paper, we study semi-total domination of Cartesian products of graphs. Our main result establishes that for any graphs $G$ and $H$, $\gamma_{t2}(G\,\square\, H)\ge \frac{1}{3}\gamma_{t2}(G)\gamma_{t2}(H)$. Comment: 9 pages |
| Databáze: | arXiv |
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