Total restrained domination in graphs of diameter 2 or 3
نویسندگان
چکیده
منابع مشابه
Total Domination in Graphs with Diameter 2
The total domination number γt (G) of a graph G is the minimum cardinality of a set S of vertices, so that every vertex of G is adjacent to a vertex in S. In this article, we determine an optimal upper bound on the total domination number of a graph with diameter 2. We show that for every graph G on n vertices with diameter 2, γt (G) ≤ 1 + √ n ln(n). This bound is optimal in the sense that give...
متن کامل$k$-tuple total restrained domination/domatic in graphs
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...
متن کاملResults 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...
متن کاملTotal restrained domination in unicyclic graphs
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...
متن کامل$k$-tuple total restrained domination/domatic in graphs
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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ژورنال
عنوان ژورنال: Mathematical Sciences
سال: 2013
ISSN: 2251-7456
DOI: 10.1186/2251-7456-7-26