Ernst J. Joubert

Learn More
Let G = (V,E) be a graph. A set S ⊆ V is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex of V − S is adjacent to a vertex in V − S. A set S ⊆ V is a restrained dominating set if every vertex in V − S is adjacent to a vertex in S and to a vertex in V − S. The total restrained domination number of G (restrained(More)
Let G = (V,E) be a graph. A set D ⊆ V is a total outer-connected dominating set of G if D is dominating and G[V −D] is connected. The total outer-connected domination number of G, denoted γtc(G), is the smallest cardinality of a total outer-connected dominating set of G. It is known that if T is a tree of order n ≥ 2, then γtc(T ) ≥ 2n 3 . We will provide a(More)
Let G = (V, E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V − S is adjacent to a vertex in S and to a vertex in V − S. The restrained domination number of G, denoted γr (G), is the smallest cardinality of a restrained dominating set of G. We will show that if G is claw-free with minimum degree at least two and G / ∈(More)
Let G = (V , E) be a graph. A set S ⊆ V is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex in V − S is adjacent to a vertex in V − S. The total restrained domination number of G, denoted γtr (G), is the smallest cardinality of a total restrained dominating set of G. We will show that if G is claw-free,(More)