Abstract
The k-restricted total domination number of a graph G is the smallest integer rk(G, γt) such that given any subset U of k vertices of G, there exists a total dominating set of G of cardinality at most rk(G, γt) containing U. Hence, the k-restricted total domination number of a graph G measures how many vertices are necessary to totally dominate a graph if an arbitrary set of k vertices must be included in the total dominating set. When k = 0, the k-restricted total domination number is the total domination number. In this paper we establish upper bound on the k-restricted total domination number of a connected graph in terms of the order and the size of the graph.
Original language | English |
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Pages (from-to) | 25-44 |
Number of pages | 20 |
Journal | Discrete Mathematics |
Volume | 289 |
Issue number | 1-3 |
DOIs | |
Publication status | Published - 28 Dec 2004 |
Externally published | Yes |
Keywords
- Bounds
- Restricted total domination number
- Total dominating set
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics