In a graph G Γ (V, E) if we think of each vertex s as the possible location for a guard capable of protecting each vertex in its closed neighborhood N[s], then ''domination'' requires every vertex to be protected. Thus, S Κ V (G) is a dominating set if Κ s β S N[s] Γ V (G). For total domination, eac
Domination and location in acyclic graphs
β Scribed by Peter J. Slater
- Publisher
- John Wiley and Sons
- Year
- 1987
- Tongue
- English
- Weight
- 439 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Let __G__ = (__V, E__) be a connected graph. A set __D__ β __V__ is a __setβdominating set__ (sdβset) if for every set __T__ β __V__ β __D__, there exists a nonempty set __S__ β __D__ such that the subgraph γ__S__ βͺ __T__γ induced by __S__ βͺ __T__ is connected. The setβdomination number
## Abstract A set __D__ of vertices in a graph is said to be a dominating set if every vertex not in __D__ is adjacent to some vertex in __D.__ The domination number Ξ²(__G__) of a graph __G__ is the size of a smallest dominating set. __G__ is called domination balanced if its vertex set can be part