A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G is the minimum cardinality of a double dominating set of G. For a graph G=(V,E), a subset D subseteq V(G) is a 2-dominating set if every vertex of V(G)D has at least two neighbors in D, while it is a 2-outer-independent dominating set of G if additionally the set V(G)D is independent. The 2-outer-independent domination number of G is the minimum cardinality of a 2-outer-independent dominating set of G. We characterize all trees with double domination number equal to 2-outer-independent domination number plus one.
Authors
Additional information
- Category
- Publikacja w czasopiśmie
- Type
- artykuł w czasopiśmie wyróżnionym w JCR
- Language
- angielski
- Publication year
- 2012
