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
β¦ LIBER β¦
Bounds on the Total Restrained Domination Number of a Graph
β Scribed by J. H. Hattingh; E. Jonck; E. J. Joubert
- Publisher
- Springer Japan
- Year
- 2010
- Tongue
- English
- Weight
- 326 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
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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