The domination number y ( G ) of a graph G = (V E ) is the minimum cardinality of a subset of Vsuch that every vertex is either in the set or is adjacent to some vertex in the set. We show that if a connected graph G has minimum2degree two and is not one of seven exceptional graphs, then y ( g ) I ~
Domination number in graphs with minimum degree two
โ Scribed by Er Fang Shan; Moo Young Sohn; Xu Dong Yuan; Michael A. Henning
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2009
- Tongue
- English
- Weight
- 264 KB
- Volume
- 25
- Category
- Article
- ISSN
- 1439-7617
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
A dominating set for a graph G = (V, E) is a subset of vertices V โ V such that for all v โ V -V there exists some u โ V for which {v, u} โ E. The domination number of G is the size of its smallest dominating set(s). We show that for almost all connected graphs with minimum degree at least 2 and q e
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
A set S of vertices of a graph G is a total dominating set, if every vertex of V (G) is adjacent to some vertex in S. The total domination number of G, denoted by ฮณ t (G), is the minimum cardinality of a total dominating set of G. We prove that, if G is a graph of order n with minimum degree at leas