Difference between2-rainbow domination and Roman domination in graphs
نویسندگان
چکیده
منابع مشابه
On 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 کاملRoman domination in graphs
A Roman dominating function on a graph G = (V, E) is a function f : V → {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. The weight of a Roman dominating function is the value f(V ) = ∑ u∈V f(u). The minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G. In this pape...
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A Roman dominating function (RDF) on a graph $G = (V, E)$ is a labeling $f : V rightarrow {0, 1, 2}$ suchthat every vertex with label $0$ has a neighbor with label $2$. The weight of $f$ is the value $f(V) = Sigma_{vin V} f(v)$The Roman domination number, $gamma_R(G)$, of $G$ is theminimum weight of an RDF on $G$.An RDF of minimum weight is called a $gamma_R$-function.A graph G is said to be $g...
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Let $G$ be a finite and simple graph with vertex set $V(G)$. A nonnegative signed total Roman dominating function (NNSTRDF) on a graph $G$ is a function $f:V(G)rightarrow{-1, 1, 2}$ satisfying the conditionsthat (i) $sum_{xin N(v)}f(x)ge 0$ for each $vin V(G)$, where $N(v)$ is the open neighborhood of $v$, and (ii) every vertex $u$ for which $f(u...
متن کاملTotal Roman domination subdivision number in graphs
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...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2012.10.017