Abstract
For an integer k ≥ 1, a (distance) k-dominating set of a connected graph G is a set S of vertices of G such that every vertex of V (G) \ S is at distance at most k from some vertex of S. The kdomination number, γk(G), of G is the minimum cardinality of a kdominating set of G. In this paper, we establish lower bounds on the k-domination number of a graph in terms of its diameter, radius, and girth. We prove that for connected graphs G and H, γk(G × H) ≥ γk(G) + γk(H) − 1, where G × H denotes the direct product of G and H.
Original language | English |
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Pages (from-to) | 11-21 |
Number of pages | 11 |
Journal | Contributions to Discrete Mathematics |
Volume | 12 |
Issue number | 2 |
Publication status | Published - 2017 |
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics