a {em roman dominating function} on a graph $g$ is a function$f:v(g)rightarrow {0,1,2}$ satisfying the condition that everyvertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex$v$ for which $f(v) =2$. {color{blue}a {em restrained roman dominating}function} $f$ is a {color{blue} roman dominating function if the vertices with label 0 inducea subgraph with no isolated vertex.} the wei...

A Roman domination function on a graph G = (V,E) is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex u with f(u) = 0 is adjacent to at least one vertex v with f(v) = 2. The weight of a Roman domination function f is the value f(V (G)) = ∑ u∈V (G) f(u). The minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G, denoted by...

A Roman dominating function (RDF) on a graph G is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex v for which f(v) = 0, is adjacent to at least one vertex u for which f(u) = 2. The weight of a Roman dominating function f is the value f(V (G)) = ∑ v∈V (G) f(v). The Roman domination number of G, denoted by γR(G), is the minimum weight of an RDF on G. For a given graph,...

A Roman dominating function of a graph G = (V,E) is a function f : V → {0, 1, 2} such that every vertex x with f(x) = 0 is adjacent to at least one vertex y with f(y) = 2. The weight of a Roman dominating function is defined to be f(V ) = P x∈V f(x), and the minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G. In this paper we answer an open pro...

A Roman dominating function on a graph G is a function f : V (G) → {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 (G)) = ∑ u∈V (G) f(u). The Roman domination number of G, γR(G), is the minimum weight of a Roman dominating function on G. In this paper, we...

A Roman dominating function on a graph G = (V,E) is a function f : V −→ {0, 1, 2} satisfying the condition that every vertex v for which f(v) = 0 is adjacent to at least one vertex u for which f(u) = 2. The weight of a Roman dominating function is the value w(f) = ∑ v∈V f(v). The Roman domination number of a graph G, denoted by γR(G), equals the minimum weight of a Roman dominating function on ...

A Roman dominating function of a graph G = (V, E) is a function f : V → {0, 1, 2} such that every vertex x with f(x) = 0 is adjacent to at least one vertex y with f(y) = 2. The weight of a Roman dominating function is defined to be f(V ) = P x∈V f(x), and the minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G. In this paper we answer an open pr...