Upper minus total domination in small-degree regular graphs
نویسندگان
چکیده
منابع مشابه
Upper minus total domination in small-degree regular graphs
A function f :V (G) → {−1, 0, 1} defined on the vertices of a graph G is a minus total dominating function (MTDF) if the sum of its function values over any open neighborhood is at least one. An MTDF f is minimal if there does not exist an MTDF g:V (G) → {−1, 0, 1}, f = g, for which g(v) f (v) for every v ∈ V (G). The weight of an MTDF is the sum of its function values over all vertices. The mi...
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A function f defined on the vertices of a graph G = (V ,E), f : V → {−1, 0, 1} is a total minus dominating function (TMDF) if the sum of its values over any open neighborhood is at least one. The weight of a TMDF is the sum of its function values over all vertices. The total minus domination number, denoted by −t (G), of G is the minimum weight of a TMDF on G. In this paper, a sharp lower bound...
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Let $D=(V,A)$ be a finite simple directed graph. A function$f:Vlongrightarrow {-1,0,1}$ is called a twin minus dominatingfunction (TMDF) if $f(N^-[v])ge 1$ and $f(N^+[v])ge 1$ for eachvertex $vin V$. The twin minus domination number of $D$ is$gamma_{-}^*(D)=min{w(f)mid f mbox{ is a TMDF of } D}$. Inthis paper, we initiate the study of twin minus domination numbersin digraphs and present some lo...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2007
ISSN: 0012-365X
DOI: 10.1016/j.disc.2006.11.011