منابع مشابه
k-TUPLE DOMATIC IN GRAPHS
For every positive integer k, a set S of vertices in a graph G = (V;E) is a k- tuple dominating set of G if every vertex of V -S is adjacent to at least k vertices and every vertex of S is adjacent to at least k - 1 vertices in S. The minimum cardinality of a k-tuple dominating set of G is the k-tuple domination number of G. When k = 1, a k-tuple domination number is the well-studied domination...
متن کاملRoman k-Tuple Domination in Graphs
For any integer $kgeq 1$ and any graph $G=(V,E)$ with minimum degree at least $k-1$, we define a function $f:Vrightarrow {0,1,2}$ as a Roman $k$-tuple dominating function on $G$ if for any vertex $v$ with $f(v)=0$ there exist at least $k$ and for any vertex $v$ with $f(v)neq 0$ at least $k-1$ vertices in its neighborhood with $f(w)=2$. The minimum weight of a Roman $k$-tuple dominatin...
متن کامل# a 28 Integers 14 ( 2014 ) on the Prime K - Tuple Conjecture
We show that the qualitative form of the prime k-tuple conjecture implies a certain conjecture related to the least size of the interval containing exactly ` prime numbers. Also, we prove that the latter conjecture implies the prime k-tuple conjecture for some minimal admissible set. The proof is self-contained and elementary.
متن کاملK-tuple Domination in Graphs
In a graph G, a vertex is said to dominate itself and all of its neighbors. For a fixed positive integer k, the k-tuple domination problem is to find a minimum sized vertex subset in a graph such that every vertex in the graph is dominated by at least k vertices in this set. The current paper studies k-tuple domination in graphs from an algorithmic point of view. In particular, we give a linear...
متن کاملThe k-tuple domination number revisited
The following fundamental result for the domination number γ(G) of a graph G was proved by Alon and Spencer, Arnautov, Lovász and Payan: γ(G) ≤ ln(δ + 1) + 1 δ + 1 n, where n is the order and δ is the minimum degree of vertices of G. A similar upper bound for the double domination number was found by Harant and Henning [On double domination in graphs. Discuss. Math. Graph Theory 25 (2005) 29–34...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2019
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2018.09.013