## Abstract A set __S__ of vertices in a graph __G__ is a total dominating set of __G__ if every vertex of __G__ is adjacent to some vertex in __S__ (other than itself). The maximum cardinality of a minimal total dominating set of __G__ is the upper total domination number of __G__, denoted by Ξ~__
Total domination in graphs
β Scribed by E. J. Cockayne; R. M. Dawes; S. T. Hedetniemi
- Publisher
- John Wiley and Sons
- Year
- 1980
- Tongue
- English
- Weight
- 374 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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 Ξ³ 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
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
## 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 __S__ of vertices in a graph __G__ is a total dominating set of __G__ if every vertex of __G__ is adjacent to some vertex in __S__. The minimum cardinality of a total dominating set of __G__ is the total domination number Ξ³~t~(__G__) of __G__. It is known [J Graph Theory 35 (2000)