منابع مشابه
A characterization of trees with equal Roman 2-domination and Roman domination numbers
Given a graph $G=(V,E)$ and a vertex $v in V$, by $N(v)$ we represent the open neighbourhood of $v$. Let $f:Vrightarrow {0,1,2}$ be a function on $G$. The weight of $f$ is $omega(f)=sum_{vin V}f(v)$ and let $V_i={vin V colon f(v)=i}$, for $i=0,1,2$. The function $f$ is said to bebegin{itemize}item a Roman ${2}$-dominating function, if for every vertex $vin V_0$, $sum_{uin N(v)}f(u)geq 2$. The R...
متن کاملRoman Domination
In his article published in 1999, Ian Stewart discussed a strategy of Emperor Constantine for defending the Roman Empire. Motivated by this article, Cockayne et al.(2004) introduced the notion of Roman domination in graphs. Let G = (V,E) be a graph. A Roman dominating function of G is a function f : V → {0, 1, 2} such that every vertex v for which f(v) = 0 has a neighbor u with f(u) = 2. The we...
متن کاملOn 2-rainbow domination and Roman domination in graphs
A Roman dominating function of a graph G is a function f : V → {0, 1, 2} such that every vertex with 0 has a neighbor with 2. The minimum of f (V (G)) = ∑ v∈V f (v) over all such functions is called the Roman domination number γR(G). A 2-rainbow dominating function of a graphG is a function g that assigns to each vertex a set of colors chosen from the set {1, 2}, for each vertex v ∈ V (G) such ...
متن کاملMixed Roman domination and 2-independence in trees
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 کاملThresholds for Roman domination
Define a Roman dominating function (RDF) of a graph G to be a function f : V (G) → {0, 1, 2} such that every u with f(u) = 0 has a neighbor v with f(v) = 2. The weight of f , w(f), is ∑ v∈V (G) f(v). The Roman domination number of G, γR(G), is the minimum weight of an RDF of G. It is easy to see that γ(G) ≤ γR(G) ≤ 2γ(G), where γ(G) is the domination number of G. In this paper, we determine pro...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2016
ISSN: 0166-218X
DOI: 10.1016/j.dam.2015.11.013