Domination, independent domination number and 2-independence number in trees
نویسندگان
چکیده
منابع مشابه
Outer independent Roman domination number of trees
A Roman dominating function (RDF) on a graph G=(V,E) is a function f : V → {0, 1, 2} such that every vertex u for which f(u)=0 is adjacent to at least one vertex v for which f(v)=2. An RDF f is calledan outer independent Roman dominating function (OIRDF) if the set ofvertices assigned a 0 under f is an independent set. The weight of anOIRDF is the sum of its function values over ...
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A edge 2-rainbow dominating function (E2RDF) of a graph G is a function f from the edge set E(G) to the set of all subsets of the set {1,2} such that for any edge.......................
متن کاملOn trees with double domination number equal to 2-outer-independent domination number plus one
A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G is the minimum cardinality of a double dominating set of G. For a graph G = (V,E), a subset D ⊆ V (G) is a 2dominating set if every vertex of V (...
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Let $G=(V, E)$ be a simple graph with vertex set $V$ and edge set $E$. A {em mixed Roman dominating function} (MRDF) of $G$ is a function $f:Vcup Erightarrow {0,1,2}$ satisfying the condition that every element $xin Vcup E$ for which $f(x)=0$ is adjacentor incident to at least one element $yin Vcup E$ for which $f(y)=2$. The weight of anMRDF $f$ is $sum _{xin Vcup E} f(x)$. The mi...
متن کاملCharacterization of trees with equal 2-domination number and domination number plus two
Let G = (V (G), E(G)) be a simple graph, and let k be a positive integer. A subset D of V (G) is a k-dominating set if every vertex of V (G) − D is dominated at least k times by D. The k-domination number γk(G) is the minimum cardinality of a k-dominating set of G. In [5] Volkmann showed that for every nontrivial tree T, γ2(T ) ≥ γ1(T ) + 1 and characterized extremal trees attaining this bound....
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2021
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2165