Nordhaus–Gaddum results for restrained domination and total restrained domination in graphs
نویسندگان
چکیده
منابع مشابه
Results on Total Restrained Domination in Graphs
Let G = (V,E) be a graph. A set S ⊆ V (G) is a total restrained dominating set if every vertex of G is adjacent to a vertex in S and every vertex of V (G)\S is adjacent to a vertex in V (G)\S. The total restrained domination number of G, denoted by γtr(G), is the smallest cardinality of a total restrained dominating set of G. In this paper we continue the study of total restrained domination in...
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Let G = (V,E) be a graph. A set S ⊆ V is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex of V − S is adjacent to a vertex in V − S. A set S ⊆ V is a restrained dominating set if every vertex in V − S is adjacent to a vertex in S and to a vertex in V − S. The total restrained domination number of G (restrained domination number of G, respectively),...
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For a graph G = (V,E), a set D ⊆ V (G) is a total restrained dominating set if it is a dominating set and both 〈D〉 and 〈V (G)−D〉 do not have isolated vertices. The cardinality of a minimum total restrained dominating set in G is the total restrained domination number. A set D ⊆ V (G) is a restrained dominating set if it is a dominating set and 〈V (G) − D〉 does not contain an isolated vertex. Th...
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For any integer $kgeq 1$, a set $S$ of vertices in a graph $G=(V,E)$ is a $k$-tuple total dominating set of $G$ if any vertex of $G$ is adjacent to at least $k$ vertices in $S$, and any vertex of $V-S$ is adjacent to at least $k$ vertices in $V-S$. The minimum number of vertices of such a set in $G$ we call the $k$-tuple total restrained domination number of $G$. The maximum num...
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Let G = (V,E) be a graph. A set S ⊆ V is a total restrained dominating set if every vertex in V is adjacent to a vertex in S and every vertex of V −S is adjacent to a vertex in V −S. The total restrained domination number of G, denoted by γtr(G), is the minimum cardinality of a total restrained dominating set of G. A unicyclic graph is a connected graph that contains precisely one cycle. We sho...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.03.061