A {em Roman dominating function} on a graph $G = (V ,E)$ is a function $f : Vlongrightarrow {0, 1, 2}$ 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 {em weight} of a Roman dominating function is the value $w(f)=sum_{vin V}f(v)$. The Roman domination number of a graph $G$, denoted by $gamma_R(G)$, equals the minimum weight of a Roman dominating function on G. The Roman game domination subdivision number of a graph $G$ is defined by the following game. Two players $mathcal D$ and $mathcal A$, $mathcal D$ playing first, alternately mark or subdivide an edge of $G$ which is not yet marked nor subdivided. The game ends when all the edges of $G$ are marked or...
AbstractA Roman dominating function of a graph G=(V,E) is a function f:V→{0,1,2} such that every ver...
A Roman dominating function of a graph ▫$G = (V,E)$▫ is a function ▫$f colon V to {0,1,2}$▫ such tha...
A Roman dominating function of a graph G is a function f : V (G) → {0, 1, 2} such that whenever f(v)...
The subdivision graph ()S G of a graph G is the graph whose vertex set is the union of the set of ve...
A Roman dominating function on a graph G =(V,E) is a function f: V →{0, 1, 2} satisfying the conditi...
AbstractA Roman dominating function of a graph G is a function f:V(G)→{0,1,2} such that whenever f(v...
AbstractLet G=(V,E) be a simple graph. A subset S⊆V is a dominating set of G, if for any vertex u∈V-...
Abstract. Roman dominating function of a graph G is a labeling function f: V (G) → {0, 1, 2} such th...
AbstractA Roman domination function on a graph G=(V(G),E(G)) is a function f:V(G)→{0,1,2} satisfying...
A Roman dominating function (RDF) on a graph G = (V,E) is a function f: V → {0,1,2} satisfying the c...
A {\em Roman dominating function} on a graph $G$ is a function $f:V(G)\rightarrow \{0,1,2\}$ sati...
A Roman dominating function (RDF) on a graph G = (V,E) is defined to be a function satisfying the co...
A Roman dominating function on a graph G is a function {}: 0,1,2f V → satisfying the condition that...
AbstractA Roman dominating function of a graph G is a labeling f:V(G)⟶{0,1,2} such that every vertex...
A Roman dominating function on a graph G = (V, E) is a function f:V (G) → {0, 1, 2} such that every ...
AbstractA Roman dominating function of a graph G=(V,E) is a function f:V→{0,1,2} such that every ver...
A Roman dominating function of a graph ▫$G = (V,E)$▫ is a function ▫$f colon V to {0,1,2}$▫ such tha...
A Roman dominating function of a graph G is a function f : V (G) → {0, 1, 2} such that whenever f(v)...
The subdivision graph ()S G of a graph G is the graph whose vertex set is the union of the set of ve...
A Roman dominating function on a graph G =(V,E) is a function f: V →{0, 1, 2} satisfying the conditi...
AbstractA Roman dominating function of a graph G is a function f:V(G)→{0,1,2} such that whenever f(v...
AbstractLet G=(V,E) be a simple graph. A subset S⊆V is a dominating set of G, if for any vertex u∈V-...
Abstract. Roman dominating function of a graph G is a labeling function f: V (G) → {0, 1, 2} such th...
AbstractA Roman domination function on a graph G=(V(G),E(G)) is a function f:V(G)→{0,1,2} satisfying...
A Roman dominating function (RDF) on a graph G = (V,E) is a function f: V → {0,1,2} satisfying the c...
A {\em Roman dominating function} on a graph $G$ is a function $f:V(G)\rightarrow \{0,1,2\}$ sati...
A Roman dominating function (RDF) on a graph G = (V,E) is defined to be a function satisfying the co...
A Roman dominating function on a graph G is a function {}: 0,1,2f V → satisfying the condition that...
AbstractA Roman dominating function of a graph G is a labeling f:V(G)⟶{0,1,2} such that every vertex...
A Roman dominating function on a graph G = (V, E) is a function f:V (G) → {0, 1, 2} such that every ...
AbstractA Roman dominating function of a graph G=(V,E) is a function f:V→{0,1,2} such that every ver...
A Roman dominating function of a graph ▫$G = (V,E)$▫ is a function ▫$f colon V to {0,1,2}$▫ such tha...
A Roman dominating function of a graph G is a function f : V (G) → {0, 1, 2} such that whenever f(v)...