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Twin signed double Roman domination numbers in directed graphs

Discrete Mathematics, Algorithms and Applications, 2022
Let [Formula: see text] be a finite simple directed graph (shortly digraph). A function [Formula: see text] is called a twin signed double Roman dominating function (TSDRDF) if (i) every vertex [Formula: see text] with [Formula: see text] has at least two in-neighbor assigned a 2 or at least an in-neighbor [Formula: see text] with [Formula: see text],
Akram Mahmoodi, Maryam Atapour, Sattar Aliyar   +2 more
openaire   +2 more sources

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

Roman Domination and Double Roman Domination Numbers of Sierpiński Graphs $$S(K_n,t)$$

Bulletin of the Malaysian Mathematical Sciences Society, 2021
Sierpiński graph \(S_n^t\) can be defined recursively as \(S_n^1\cong K_n\) and one obtains \(S_n^{t+1}\) from \(S_n^t\) by replacing each vertex from \(S_n^t\) by a copy of \(K_n\) and adding some special edges between these copies of \(K_n\). Let \(G\) be a graph.
openaire   +2 more sources

Inverse double Roman domination in graphs

Discret. Math. Algorithms Appl., 2022
For a graph [Formula: see text], a double Roman dominating function (DRDF) is a function [Formula: see text] such that each vertex [Formula: see text] with [Formula: see text] is adjacent to at least two vertices labeled [Formula: see text] or one vertex
Wilma Laveena D' Souza, V. Chaitra, M. Kumara   +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

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

Double Roman Domination in Cartesian Product

Creative Mathematics and Informatics
Given a graph $G=(V,E)$, a function $f:V\rightarrow \{0,1,2,3\}$ having the property that if $f(v)=0$, then there exist $ v_{1},v_{2}\in N(v)$ such that $f(v_{1})=2=f(v_{2})$ or there exists $ w \in N(v)$ such that $f(w)=3$, and if $f(v)=1$, then there ...
V. Anu, L. Aparna
semanticscholar   +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

Discharging Approach for Double Roman Domination in Graphs

IEEE Access, 2018
Zehui Shao, Pu Wu, Huiqin Jiang
exaly  

Independent Double Roman Domination in Graphs

Bulletin of the Iranian Mathematical Society, 2019
H R Maimani, S M Sheikholeslami, Sheikholeslami Seyed Mahmoud   +2 more
exaly