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Total double Roman domination in graphs [PDF]

Communications in Combinatorics and Optimization, 2020
Let $G$ be a simple graph with vertex set $V$. A double Roman dominating function (DRDF) on $G$ is a function $f:V\rightarrow\{0,1,2,3\}$ satisfying that if $f(v)=0$, then the vertex $v$ must be adjacent to at least two vertices assigned $2$ or one ...
Guoliang Hao, Lutz Volkmann, Doost Ali Mojdeh   +2 more
doaj   +3 more sources

Bounds on signed total double Roman domination [PDF]

Communications in Combinatorics and Optimization, 2020
A signed total double Roman dominating function (STDRDF) on {an} isolated-free graph $G=(V,E)$ is a function $f:V(G)\rightarrow\{-1,1,2,3\}$ such that (i) every vertex $v$ with $f(v)=-1$ has at least two neighbors assigned 2 under $f$ or one neighbor ...
L. Shahbazi, H. Abdollahzadeh Ahangar, R. Khoeilar, S.M. Sheikholeslami   +3 more
doaj   +3 more sources

On the Total Double Roman Domination [PDF]

IEEE Access, 2019
Let G = (V, E) be a simple graph. A double Roman dominating function (DRDF) on G is a function f from the vertex set V of G into {0, 1, 2, 3} such that if f (u) = 0, then u must have at least two neighbors assigned 2 or one neighbor assigned 3 under f ...
Zehui Shao, Jafar Amjadi, Seyed Mahmoud Sheikholeslami, Mina Valinavaz   +3 more
doaj   +3 more sources

Quasi total double Roman domination in graphs [PDF]

AKCE International Journal of Graphs and Combinatorics
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 f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w
S. Kosari, S. Babaei, J. Amjadi, M. Chellali, S. M. Sheikholeslami   +4 more
doaj   +3 more sources

On the Outer Independent Total Double Roman Domination in Graphs [PDF]

Mediterranean Journal of Mathematics, 2023
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H. Abdollahzadeh Ahangar, Mustapha Chellali, Seyed Mahmoud Sheikholeslami, J.C. Valenzuela   +3 more
openalex   +4 more sources

Bounds on the total double Roman domination number of graphs [PDF]

Discussiones Mathematicae Graph Theory, 2021
Summary: Let \(G\) be a simple graph with no isolated vertex and let \(\gamma_{tdR}(G)\) be the total double Roman domination number of \(G\). In this paper, we present lower and upper bounds on \(\gamma_{tdR}(G)\) of a graph \(G\) in terms of the order, open packing number and the numbers of support vertices and leaves, and we characterize all ...
Guoliang Hao, Zhihong Xie, Seyed Mahmoud Sheikholeslami, M. Hajjari   +3 more
openalex   +2 more sources

Quasi total double Roman domination stability in graphs

AKCE International Journal of Graphs and Combinatorics
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 [Formula: see text] if [Formula: see text], then the vertex v must have at least two neighbors ...
Saeed Kosari, Hanxin Jiang, M. Esmaeili
doaj   +2 more sources

Signed total double Roman dominating functions in graphs

AKCE International Journal of Graphs and Combinatorics
A signed total double Roman dominating function (STDRDF) on an isolated-free graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex v with [Formula: see text] has at least two neighbors assigned 2 under f or one neighbor w
L. Shahbazi, H. Abdollahzadeh Ahangar, S. M. Sheikholeslami   +2 more
doaj   +2 more sources

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. In this work, we focus on the quasi total double Roman domination problem (QTDRDP), a combinatorial optimization problem ...
Charan Karnati, Alfred Raju M., Palagiri Venkata Subba Reddy   +2 more
openalex   +3 more sources

Lower Bounds on Signed Total Double Roman k-domination in Graphs [PDF]

Journal of Mathematical Sciences and Informatics
L. Shahbazi, H. Abdollahzadeh Ahangar, R. Khoeilar, Seyed Mahmoud Sheikholeslami   +3 more
openalex   +2 more sources