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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   +5 more sources

Quasi total double Roman domination 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 (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   +5 more sources

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

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   +3 more sources

Bounds on the total double Roman domination number of graphs

Discussiones Mathematicae Graph Theory, 2023
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 ...
Hao, Guoliang, Xie, Zhihong, Sheikholeslami, Seyed Mahmoud, Hajjari, Maryam   +3 more
openaire   +2 more sources

On the Outer Independent Total Double Roman Domination in Graphs

Mediterranean Journal of Mathematics, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abdollahzadeh Ahangar, H., Chellali, Mustapha, Sheikholeslami, Seyed Mahmoud, Valenzuela Tripodoro, Juan Carlos   +3 more
openaire   +4 more sources

Domination parameters with number : Interrelations and algorithmic consequences [PDF]

Discrete Applied Mathematics, 2015
In this paper, we study the most basic domination invariants in graphs, in which number 2 is intrinsic part of their definitions. We classify them upon three criteria, two of which give the following previously studied invariants: the weak $2$-domination
Flavia Bonomo, B. Brešar, L. N. Grippo, Martin Milanič, M. Safe   +4 more
semanticscholar   +5 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

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
openaire   +3 more sources