On perfect and quasiperfect dominations in graphs
نویسندگان
چکیده
منابع مشابه
On Perfect and Quasiperfect Dominations in Graphs∗
A subset S ⊆ V in a graph G = (V,E) is a k-quasiperfect dominating set (for k ≥ 1) if every vertex not in S is adjacent to at least one and at most k vertices in S. The cardinality of a minimum k-quasiperfect dominating set in G is denoted by γ 1k (G). Those sets were first introduced by Chellali et al. (2013) as a generalization of the perfect domination concept and allow us to construct a dec...
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A k−quasiperfect dominating set (k ≥ 1) of a graph G is a vertex subset S such that every vertex not in S is adjacent to at least one and at most k vertices in S. The cardinality of a minimum k-quasiperfect dominating set in G is denoted by γ 1k (G). Those sets were first introduced by Chellali et al. (2013) as a generalization of the perfect domination concept. The quasiperfect domination chai...
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Nine variations of the concept of domination in a simple graph are identified as fundamental domination concepts, and a unified approach is introduced for studying them. For each variation, the minimum cardinality of a subset of dominating elements is the corresponding fundamental domination number. It is observed that, for each nontrivial connected graph, at most five of these nine numbers can...
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Let $G=(V(G),E(G))$ be a graph, $gamma_t(G)$. Let $ooir(G)$ be the total domination and OO-irredundance number of $G$, respectively. A total dominating set $S$ of $G$ is called a $textit{total perfect code}$ if every vertex in $V(G)$ is adjacent to exactly one vertex of $S$. In this paper, we show that if $G$ has a total perfect code, then $gamma_t(G)=ooir(G)$. As a consequence, ...
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ژورنال
عنوان ژورنال: Filomat
سال: 2017
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1702413c