The k-domination number of a graph is the cardinality of a smallest set of vertices such that every vertex not in the set is adjacent to at least k vertices of the set. We prove two bounds on the k-domination number of a graph, inspired by two conjectures of the computer program Graffiti.pc. In part
Bounds on the Distance Two-Domination Number of a Graph
β Scribed by N. Sridharan; V.S.A. Subramanian; M.D. Elias
- Publisher
- Springer Japan
- Year
- 2002
- Tongue
- English
- Weight
- 122 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
For r > 0, let the r-domination number of a graph, d,, be the size of a smallest set of vertices such that every vertex of the graph is within distance r of a vertex in that set. This paper contains proofs that every graph with a spanning tree with at least n/2 leaves has d, s n/(2r); this compares
Topp, J. and L. Volkmann, Some upper bounds for the product of the domination number and the chromatic number of a graph, Discrete Mathematics 118 (1993) 2899292. Some new upper bounds for yx are proved, where y is the domination number and x is the chromatic number of a graph. All graphs consider