Signed 2-domination in caterpillars

Bohdan Zelinka

Displaying similar documents to “Signed 2-domination in caterpillars”

Domination in graphs with few edges

Bohdan Zelinka (1995)

Mathematica Bohemica

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The domination number $(G)$ of a graph $G$ and two its variants are considered, namely the signed domination number $_{s} (G)$ and the minus domination number $^{-} (G)$ . These numerical invariants are compared for graphs in which the degrees of vertices do not exceed 3.

Minus total domination in graphs

Hua Ming Xing, Hai-Long Liu (2009)

Czechoslovak Mathematical Journal

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A three-valued function $f V \to {- 1, 0, 1}$ 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 $v \in V$ , $f (N (v)) \geq 1$ , where $N (v)$ consists of every vertex adjacent to $v$ . The weight of an MTDF is $f (V) = \sum f (v)$ , over all vertices $v \in V$ . 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...

On total restrained domination in graphs

De-xiang Ma, Xue-Gang Chen, Liang Sun (2005)

Czechoslovak Mathematical Journal

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In this paper we initiate the study of total restrained domination in graphs. Let $G = (V, E)$ be a graph. A total restrained dominating set is a set $S \subseteq V$ where every vertex in $V - S$ is adjacent to a vertex in $S$ as well as to another vertex in $V - S$ , and every vertex in $S$ is adjacent to another vertex in $S$ . The total restrained domination number of $G$ , denoted by $γ_{r}^{t} (G)$ , is the smallest cardinality of a total restrained dominating set of $G$ . First, some exact values and sharp bounds for $γ_{r}^{t} (G)$ are given in Section 2....