Results 231 to 240 of about 107,030 (250)

Outer independent double Roman domination in unicyclic and bicyclic graphs

Ars Combinatoria
An outer independent double Roman dominating function (OIDRDF) of a graph \( G \) is a function \( f:V(G)\rightarrow\{0,1,2,3\} \) satisfying the following conditions: (i) every vertex \( v \) with \( f(v)=0 \) is adjacent to a vertex assigned 3 or at least two vertices assigned 2; (ii) every vertex \( v \) with \( f(v)=1 \) has a neighbor assigned 2 ...
Nazari-Moghaddam, S., Chellali, M., Sheikholeslami, S. M.   +2 more
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Algorithmic Aspects of Outer-Independent Double Roman Domination in Graphs

International Journal of Foundations of Computer Science
Let [Formula: see text] be graph. For any function [Formula: see text], let [Formula: see text], [Formula: see text]. The function [Formula: see text] is called an outer-independent double Roman dominating function (OIDRDF) if the following conditions are satisfied.
Amit Sharma, P. Venkata Subba Reddy, S. Arumugam, Jakkepalli Pavan Kumar   +3 more
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Further results on the independent roman domination number of graphs

Quaestiones Mathematicae, 2023
Let f : V (G) → {0, 1, 2} be a function on a graph G with vertex set V (G). Let Vi = {v ∈ V (G) : f(v) = i} for every i ∈ {0, 1, 2}. The function f is said to be an independent Roman dominating function on G if V1 ∪ V2 is an independent set and N(v) ∩ V2 ̸= ∅ for every v ∈ V0.
Mart'ınez, Abel Cabrera, Mira, Frank A. Hernandez   +1 more
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More results on the outer-independent triple Roman domination number

Discrete Mathematics, Algorithms and Applications
An outer-independent triple Roman dominating function (OI[3]RDF) on a graph [Formula: see text] is function [Formula: see text] having the property that (i) if [Formula: see text] then [Formula: see text] must have either a neighbor assigned 4 or two neighbors one of which is assigned 3 and the other at least 2 or [Formula: see text] has three ...
S. Babaei, J. Amjadi, M. Chellali, S. M. Sheikholeslami   +3 more
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Independent Signed Double Roman Domination

Advances in Applied Mathematics
柠 李
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Total Roman domination and 2-independence in trees

2023
Summary: Let \(G = (V, E)\) be a simple graph with vertex set \(V\) and edge set \(E\). A {\em total Roman dominating function} on a graph \(G\) is a function \(f: V\rightarrow\{0, 1, 2\}\) satisfying the following conditions: (i) every vertex \(u\) such that \(f(u) = 0\) is adjacent to at least one vertex \(v\) such that \(f(v) = 2\) and (ii) the ...
Abdollahzadeh Ahangar, Hossein, Soroudi, Marzieh, Amjadi, Jafar, Sheikholeslami, Seyed Mahmoud   +3 more
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Roman domination and 2-independence in trees

Discrete Mathematics, Algorithms and Applications, 2017
A Roman dominating function (RDF) on a graph [Formula: see text] is a function [Formula: see text] satisfying the condition that every vertex [Formula: see text] with [Formula: see text] is adjacent to at least one vertex [Formula: see text] of [Formula: see text] for which [Formula: see text].
Meddah, Nacéra, Chellali, Mustapha
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Outer independent Roman dominating functions in graphs

International Journal of Computer Mathematics, 2017
ABSTRACTA Roman dominating function (RDF) 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. A function f:V(G)→{0,1,2} is an outer-independent Roman dominating function (OIRDF) on G if f is an RDF and V0 is an independent set.
Hossein Abdollahzadeh Ahangar, Mustapha Chellali, Vladimir Samodivkin   +2 more
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(Independent) Roman {2}-Domination Number on Graphs

Journal of Interconnection Networks (JOIN)
For a graph [Formula: see text], a function [Formula: see text] is a Roman {2}-dominating function (R{2}DF) if [Formula: see text] satisfies the following condition: if [Formula: see text] then there is [Formula: see text] such that [Formula: see text ...
Yulan Hu, Luyao Yang, Weihua Yang
semanticscholar   +1 more source

Outer independent triple Roman domination

Asian-European Journal of Mathematics
An outer-independent triple Roman dominating function (OI[3]RDF) on a graph G = (V, E) is a function f : V → {0, 1, 2, 3, 4} having the property that (i) if f (v) = 0, then v must have either a neighbor assigned 4 or two neighbors one of which is ...
J. Amjadi, F. Najafi, M. Chellali, S. M. Sheikholeslami   +3 more
semanticscholar   +1 more source