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...
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 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 کاملResults on Total Domination and Total Restrained Domination in Grid Graphs
A set S of vertices in a graph G(V,E) is called a total dominating set if every vertex v ∈ V is adjacent to an element of S. A set S of vertices in a graph G(V,E) is called a total restrained dominating set if every vertex v ∈ V is adjacent to an element of S and every vertex of V − S is adjacent to a vertex in V − S. The total domination number of a graph G denoted by γt(G) is the minimum card...
متن کاملOn the total restrained domination edge critical graphs
Let G = (V, E) be a graph. A set D ⊆ V is a total restrained dominating set of G if every vertex in V has a neighbor in D and every vertex in V −D has a neighbor in V −D. The cardinality of a minimum total restrained dominating set in G is the total restrained domination number of G. In this paper, we define the concept of total restrained domination edge critical graphs, find a lower bound for...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2005
ISSN: 0011-4642,1572-9141
DOI: 10.1007/s10587-005-0012-2