A survey of selected recent results on total domination in graphs - ScienceDirect Skip to main
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Abstract In 1985, Fink and Jacobson gave a generalization of the concepts of domination
and independence in graphs. For a positive integer k, a subset S of vertices in a graph G=(V …

Let G=(V, E) be a graph; a set S⊆ V is a total k-dominating set if every vertex v∈ V has at
least k neighbors in S. The total k-domination number γ kt (G) is the minimum cardinality …

Efficient open domination in graph products Page 1 Discrete Mathematics and Theoretical
Computer Science DMTCS vol. 16:1, 2014, 105–120 Efficient open domination in graph …

An upper bound for the domination number of the direct product of graphs is proved. It in
particular implies that for any graphs G and H, γ (G× H)⩽ 3γ (G) γ (H). Graphs with arbitrarily …

Let G be a graph and let D be a subset of its vertex set. D is called k-dominating if| N (v)∩
D|≥ k for all v∈ V (G)∖ D; D is called k-tuple dominating if| N v∩ D|≥ k for all v∈ V (G); and …

Let G be a graph with no isolated vertex and f: V (G)→{0, 1, 2} a function. If f satisfies that
every vertex in the set {v∈ V (G): f (v)= 0} is adjacent to at least one vertex in the set {v∈ V …

A sharp lower bound for the domination number and the total domination number of the
direct product of finitely many complete graphs is given:[Formula: see text]. Sharpness is …

A set S of vertices of a graph G is a dominating set in G if every vertex outside of S is
adjacent to at least one vertex belonging to S. A domination parameter of G is related to …

Abstract Let G=(V, E) G=(V, E) be a graph. A set S ⊆ VS⊆ V is a total k-dominating set if
every vertex v ∈ V v∈ V has at least k neighbors in S. The total k-domination number γ _ kt …