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Exploring Variant Roman Domination Number in Complete Binary Trees Using Python Programming

2024 International Conference on Sustainable Communication Networks and Application (ICSCNA)
A Roman Dominating Function (RDF) on a graph $G$ is defined as a function $g$ that assigns a value of 0, 1, or 2 to each vertex in such a way that any vertex assigned a value of 0 is adjacent to at least one vertex assigned a value of 2. The total weight
J. Meena, T. Mai
semanticscholar   +1 more source

(Independent) Roman Domination Parameterized by Distance to Cluster

International Conference on Combinatorial Optimization and Applications
Given a graph $G=(V,E)$, a function $f:V\to \{0,1,2\}$ is said to be a \emph{Roman Dominating function} (RDF) if for every $v\in V$ with $f(v)=0$, there exists a vertex $u\in N(v)$ such that $f(u)=2$.
Pradeesha Ashok, G. K. Das, Arti Pandey, Kaustav Paul, Subhabrata Paul   +4 more
semanticscholar   +1 more source

Mixed Roman Domination in Graphs

Bulletin of the Malaysian Mathematical Sciences Society, 2015
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Ahangar, H. Abdollahzadeh, Haynes, Teresa W., Valenzuela-Tripodoro, J. C.   +2 more
openaire   +3 more sources

On Total Roman Domination in Graphs

2017
A Roman dominating function (RDF) on a graph \(G = (V,E)\) is a function \( f:V \rightarrow \lbrace 0,1,2\rbrace \) 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 total Roman dominating function on a graph \(G = (V,E)\) is a Roman dominating function \(f : V \rightarrow ...
P. Roushini Leely Pushpam, Padmapriea Sampath   +1 more
openaire   +1 more source

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 ...
Amit Sharma, P. V. S. Reddy, Subramanian Arumugam, J. P. Kumar   +3 more
semanticscholar   +1 more source

Majority Roman domination in graphs

Discrete Mathematics, Algorithms and Applications, 2020
A Majority Roman Dominating Function (MRDF) on a graph [Formula: see text] is a function [Formula: see text] satisfying the conditions that (i) the sum of its function values over at least half the closed neighborhood is at least one and (ii) every vertex [Formula: see text] for which [Formula: see text] is adjacent to at least one vertex [Formula ...
openaire   +2 more sources

On the complexity of perfect Roman domination and perfect double Roman domination

Discrete Mathematics, Algorithms and Applications
For a graph [Formula: see text] and a function [Formula: see text], let [Formula: see text] ([Formula: see text]) be the set of vertices assigned the value [Formula: see text] by [Formula: see text]. A perfect Roman dominating function on a graph [Formula: see text] is a function [Formula: see text] satisfying the condition that every vertex [Formula ...
Seyed Hosein Mirhoseini, Nader Jafari Rad, Noor A’lawiah Abd Aziz, Hailiza Kamarulhaili   +3 more
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Total Roman {2}-domination in graphs

Quaestiones Mathematicae, 2021
Ismael G Yero, Suitberto Cabrera, Abel Cabrera Martinez   +2 more
exaly  

Roman {3}-domination (double Italian domination)

Discrete Applied Mathematics, 2020
Doost Ali Mojdeh, Lutz Volkmann
exaly  

Double Roman domination stability in graphs

Discrete Applied Mathematics
Zhuang Wei
semanticscholar   +1 more source