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
The cototal domination number of a graph
β Scribed by Kulli, V. R.; Janakiram, B.; Iyer, Radha R.
- Book ID
- 120618876
- Publisher
- Informa UK (Taylor & Francis)
- Year
- 1999
- Tongue
- English
- Weight
- 271 KB
- Volume
- 2
- Category
- Article
- ISSN
- 0972-0529
No coin nor oath required. For personal study only.
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
The closed neighborhood of a vertex subset S of a graph G = (V,E), denoted as N[Sj, is defined ss the union of S and the set of all the vertices adjacent to some vertex of S. A dominating set of a graph G = (V, E) is defined as a set S of vertices such that N[q = V. The domination number of a graph