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Bounds on the Total Restrained Domination Number of a Graph

✍ 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

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Bounds on the -domination number of a gr
✍ Ermelinda DeLaViΓ±a; Wayne Goddard; Michael A. Henning; Ryan Pepper; Emil R. Vaug πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 200 KB

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

On the r-domination number of a graph
✍ Jerrold R. Griggs; Joan P. Hutchinson πŸ“‚ Article πŸ“… 1992 πŸ› Elsevier Science 🌐 English βš– 468 KB

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