On the domination of triangulated discs
| Autor: | Noor A'lawiah Abd Aziz, Nader Jafari Rad, Hailiza Kamarulhaili |
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| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Mathematica Bohemica, Vol 148, Iss 4, Pp 555-560 (2023) |
| Druh dokumentu: | article |
| ISSN: | 0862-7959 2464-7136 |
| DOI: | 10.21136/MB.2022.0122-21 |
| Popis: | Let $G$ be a $3$-connected triangulated disc of order $n$ with the boundary cycle $C$ of the outer face of $G$. Tokunaga (2013) conjectured that $G$ has a dominating set of cardinality at most $\frac14(n+2)$. This conjecture is proved in Tokunaga (2020) for $G-C$ being a tree. In this paper we prove the above conjecture for $G-C$ being a unicyclic graph. We also deduce some bounds for the double domination number, total domination number and double total domination number in triangulated discs. |
| Databáze: | Directory of Open Access Journals |
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