Probabilistic Bounds On Weak and Strong Total Domination in Graphs

A set D of vertices in a graph G = (V,E) is a total dominating set if every vertex of G is adjacent to some vertex in D. A total dominating set D of G is said to be weak if every vertex v ∈ V -D is adjacent to a vertex u ∈ D such that dG(v) ≥ dG(u). The weak total domination number γwt of G is the m...

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Bibliographic Details
Published inInternational journal of mathematical combinatorics Vol. 1; p. 97
Main Author Akhbari, M H
Format Journal Article
LanguageEnglish
Published Gallup Science Seeking - distributor 01.03.2016
Subjects
Geometry
Graph theory
Graphs
Mathematics
Probability
Upper bounds
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Summary:A set D of vertices in a graph G = (V,E) is a total dominating set if every vertex of G is adjacent to some vertex in D. A total dominating set D of G is said to be weak if every vertex v ∈ V -D is adjacent to a vertex u ∈ D such that dG(v) ≥ dG(u). The weak total domination number γwt of G is the minimum cardinality of a weak total dominating set of G. A total dominating set D of G is said to be strong if every vertex v ∈ V - D is adjacent to a vertex u ∈ D such that dG(v) ≤ dG(u). The strong total domination number γst(G) of G is the minimum cardinality of a strong total dominating set of G. We present probabilistic upper bounds on weak and strong total domination number of a graph.
ISSN:1937-1055
1937-1047