Abstract
Let k be a positive integer and G be a connected graph. This paper considers the relations among four graph theoretical parameters: the k-domination number γk (G), the connected k-domination number γkc (G); the k-independent domination number γki (G) and the k-irredundance number irk (G). The authors prove that if an irk-set X is a k-independent set of G, then irk (G) = γk (G) = γki (G), and that for k ≥ 2, γkc (G) = 1 if irk (G) = 1, γkc (G) ≤ max { (2 k + 1) irk (G) - 2 k, frac(5, 2) irk (G) k - frac(7, 2) k + 2 } if irk (G) is odd, and γkc (G) ≤ frac(5, 2) irk (G) k - 3 k + 2 if irk (G) is even, which generalize some known results.
Original language | English (US) |
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Pages (from-to) | 2943-2953 |
Number of pages | 11 |
Journal | Discrete Mathematics |
Volume | 306 |
Issue number | 22 |
DOIs | |
State | Published - Nov 28 2006 |
Externally published | Yes |
Keywords
- Connected k-domination number
- k-Domination number
- k-Independent domination number
- k-Independent set
- k-Irredundance number
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics