نتایج جستجو برای: tuple total restrained domination number
تعداد نتایج: 1842615 فیلتر نتایج به سال:
In this paper, we provide an upper bound for the k-tuple domination number that generalises known upper bounds for the double and triple domination numbers. We prove that for any graph G, ×k(G) ln( − k + 2)+ ln(∑k−1 m=1(k −m)d̂m + )+ 1 − k + 2 n, where ×k(G) is the k-tuple domination number; is the minimal degree; d̂m is the m-degree of G; = 1 if k = 1 or 2 and =−d if k 3; d is the average degree...
In a graph $G$, vertex dominates itself and its neighbours. A set $D\subseteq V(G)$ is said to be $k$-tuple dominating of $G$ if $D$ every at least $k$ times. The minimum cardinality among all sets the domination number $G$. this paper, we provide new bounds on parameter. Some these generalize other ones that have been given for case $k=2$. addition, improve two well-known lower number.
A {em Roman dominating function} on a graph $G$ is a function $f:V(G)rightarrow {0,1,2}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$. A {em total Roman dominating function} is a Roman dominating function with the additional property that the subgraph of $G$ induced by the set of all vertices of positive weight has n...
In a graph G = (V,E) a vertex is said to dominate itself and all its neighbours. A weak dominating set is a set S ⊆ V where for every vertex u not in S there is a vertex v of S adjacent to u with dG(v) 6 dG(u) . A restrained dominating set is a set S ⊆ V where every vertex in V − S is adjacent to a vertex in S as well as another vertex in V − S . The weak domination number γw(G) (resp. restrain...
Let $R$ be a commutative ring and $M$ be an $R$-module with $T(M)$ as subset, the set of torsion elements. The total graph of the module denoted by $T(Gamma(M))$, is the (undirected) graph with all elements of $M$ as vertices, and for distinct elements $n,m in M$, the vertices $n$ and $m$ are adjacent if and only if $n+m in T(M)$. In this paper we study the domination number of $T(Gamma(M))$ a...
a set $s$ of vertices of a graph $g=(v,e)$ without isolated vertex is a {em total dominating set} if every vertex of $v(g)$ is adjacent to some vertex in $s$. the {em total domatic number} of a graph $g$ is the maximum number of total dominating sets into which the vertex set of $g$ can be partitioned. we show that the total domatic number of a random $r$-regular graph is almost...
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