Domination Number, Independent Domination Number and 2-Independence Number in Trees
| Autor: | Dehgardi Nasrin, Sheikholeslami Seyed Mahmoud, Valinavaz Mina, Aram Hamideh, Volkmann Lutz |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Discussiones Mathematicae Graph Theory, Vol 41, Iss 1, Pp 39-49 (2021) |
| Druh dokumentu: | article |
| ISSN: | 2083-5892 |
| DOI: | 10.7151/dmgt.2165 |
| Popis: | For a graph G, let γ(G) be the domination number, i(G) be the independent domination number and β2(G) be the 2-independence number. In this paper, we prove that for any tree T of order n ≥ 2, 4β2(T) − 3γ(T) ≥ 3i(T), and we characterize all trees attaining equality. Also we prove that for every tree T of order n ≥ 2, i(T)≤3β2(T)4i(T) \le {{3{\beta _2}(T)} \over 4} , and we characterize all extreme trees. |
| Databáze: | Directory of Open Access Journals |
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