An upper bound on the domination number of a graph with minimum degree 2
โ Scribed by Allan Frendrup; Michael A. Henning; Bert Randerath; Preben Dahl Vestergaard
- Book ID
- 108113991
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 621 KB
- Volume
- 309
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The kdomination number of a graph G, y k ( G ) , is the least cardinality of a set U of verticies such that any other vertex is adjacent to at least k vertices of U. We prove that if each vertex has degree at least k. then YAG) 5 kp/(k + 1).
The domination number of G, denoted by ฮณ (G), is the minimum cardinality of a dominating set of G. We prove that if G is a Hamiltonian graph of order n with minimum degree at least six, then ฮณ (G) โค 6n 17 .
We prove a new upper bound on the independent domination number of graphs in terms of the number of vertices and the minimum degree. This bound is slightly better than that of Haviland (1991) and settles the case 6 = 2 of the corresponding conjecture by Favaron (1988). @ 1998 Elsevier Science B.V. A