Minus total domination in graphs |
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Authors: | Hua-Ming Xing Hai-Long Liu |
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Institution: | 1.School of Sciences,Tianjin University of Sci. & Tech., Teda,Tianjin,P.R. China;2.Dept. of Mathematics,Beijing Institute of Technology,Beijing,P.R. China |
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Abstract: | A three-valued function f: V → {−1, 0, 1} defined on the vertices of a graph G= (V, E) is a minus total dominating function (MTDF) if the sum of its function values over any open neighborhood is at least one.
That is, for every υ ∈ V, f(N(υ)) ⩾ 1, where N(υ) consists of every vertex adjacent to υ. The weight of an MTDF is f(V) = Σf(υ), over all vertices υ ∈ V. The minus total domination number of a graph G, denoted γ
t
−(G), equals the minimum weight of an MTDF of G. In this paper, we discuss some properties of minus total domination on a graph G and obtain a few lower bounds for γ
t
−(G). |
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