Domination Number, Independent Domination Number and 2-Independence Number in Trees
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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Zielona Góra
2021-02-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.2165 |
| Summary: | 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. |
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| ISSN: | 2083-5892 |