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Meta-Heuristic Algorithms for Quasi Total Double Roman Domination Problem

RAIRO - Theoretical Informatics and Applications
Ensuring the resilience and security of complex networks, such as communication or power grids, requires strategies that can withstand failures and attacks. One such approach involves the use of domination models in graph theory.
Charan Karnati, A. M, Palagiri Venkata Subba Reddy   +2 more
semanticscholar   +1 more source

Double Roman domination subdivision number in graphs

Asian-European Journal of Mathematics, 2021
For a graph [Formula: see text], a double Roman dominating function is a function [Formula: see text] having the property that if [Formula: see text], then vertex [Formula: see text] must have at least two neighbors assigned [Formula: see text] under ...
J. Amjadi, H. Sadeghi
semanticscholar   +1 more source

Bounds on the quasi total double Roman domination number in graphs

Discrete Mathematics, Algorithms and Applications (DMAA)
A quasi total double Roman dominating function (QTDRD-function) on a graph [Formula: see text] is a function [Formula: see text] having the property that (i) if [Formula: see text], then vertex [Formula: see text] must have at least two neighbors ...
J. Amjadi, S. Babaei, S. M. Sheikholeslami, M. Chellali, S. Kosari   +4 more
semanticscholar   +1 more source

On the Outer Independent Total Double Roman Domination in Graphs

Mediterranean Journal of Mathematics, 2023
A double Roman dominating function (DRDF) on a graph $$G=(V,E)$$ G = ( V , E ) is a function $$f:V\rightarrow \{0,1,2,3\}$$ f : V → { 0 , 1 , 2 , 3 } satisfying (i) if $$f(v)=0$$ f ( v ) = 0 , then there must be at least two neighbors assigned 2 under f ...
H. Ahangar, M. Chellali, S. Sheikholeslami, J. Valenzuela-Tripodoro   +3 more
semanticscholar   +1 more source

Outer independent double Roman domination in unicyclic and bicyclic graphs

Ars Comb.
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 ...
S. Nazari-Moghaddam, M. Chellali, S. Sheikholeslami   +2 more
semanticscholar   +1 more source

Algorithmic Framework for Double Roman Domination in Chemical Structures using Python

2025 3rd International Conference on Intelligent Cyber Physical Systems and Internet of Things (ICoICI)
This paper focuses on the double Roman domination number, a graph-theoretic parameter defined through the double Roman dominating function h : V → {0, 1, 2, 3}.
st J. Meena, N. M. Malini, D. Yoga, Pradeesh Kumar   +3 more
semanticscholar   +1 more source

On the double Roman domination number in trees [PDF]

Australas. J Comb., 2020
Summary: For a graph \(G\), let \(\gamma_{dR}(G)\) and \(\gamma_R(G)\) denote the double Roman domination number and the Roman domination number, respectively. In this paper, we show that for every tree \(T\) of order \(n\geq 3\), with \(\ell(T)\) leaves and \(s(T)\) support vertices, \begin{align*} \gamma_R(T)+\lceil & \frac{\ell(T)-s(T)}{\Delta(T ...
Sakineh Nazari-Moghaddam, Mustapha Chellali   +1 more
openaire   +1 more source

Critical concept for double Roman domination in graphs

Discrete Mathematics, Algorithms and Applications, 2020
A double Roman dominating function (DRDF) on a graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex [Formula: see text] with [Formula: see text] is adjacent to at least two vertices assigned a [Formula: see text] or to at least one vertex assigned a [Formula: see text] and (ii) every vertex [Formula: see text] with ...
Sakineh Nazari-Moghaddam, Lutz Volkmann
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

Outer independent signed double Roman domination

Journal of Applied Mathematics and Computing, 2021
Suppose $$[3]=\{0,1,2,3\}$$ and $$[3^{-}]=\{-1,1,2,3\}$$ . An outer independent signed double Roman dominating function (OISDRDF) of a graph
Hossein Abdollahzadeh Ahangar, Fatemeh Nahani Pour, Mustapha Chellali, Seyed Mahmoud Sheikholeslami   +3 more
openaire   +1 more source