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Total Roman Domination Number of Rooted Product Graphs [PDF]

Mathematics, 2020
Let G be a graph with no isolated vertex and f:V(G)→{0,1,2} a function. If f satisfies that every vertex in the set {v∈V(G):f(v)=0} is adjacent to at least one vertex in the set {v∈V(G):f(v)=2}, and if the subgraph induced by the set {v∈V(G):f(v)≥1} has ...
Abel Cabrera Martínez, Suitberto Cabrera García, Andrés Carrión García, Frank A. Hernández Mira   +3 more
doaj   +3 more sources

Total Roman domination in the lexicographic product of graphs [PDF]

Discrete Applied Mathematics, 2019
A total Roman dominating function of a graph $G=(V,E)$ is a function $f: V(G)\to \{0,1,2\}$ such that for every vertex $v$ with $f(v)=0$ there exists a vertex $u$ adjacent to $v$ with $f(u)=2$, and such that the subgraph induced by the set of vertices labeled one or two has no isolated vertices.
Nicolás Campanelli, Dorota Kuziak
openaire   +4 more sources

Outer-independent total Roman domination in graphs [PDF]

Discrete Applied Mathematics, 2019
Given a graph $G$ with vertex set $V$, a function $f:V\rightarrow \{0,1,2\}$ is an outer-independent total Roman dominating function on $G$ if \begin{itemize} \item every vertex $v\in V$ for which $f(v)=0$ is adjacent to at least one vertex $u\in V$ such that $f(u)=2$, \item every vertex $x\in V$ for which $f(x)\ge 1$ is adjacent to at least one vertex
Abel Cabrera Martínez, Dorota Kuziak, Ismael González Yero   +2 more
openaire   +4 more sources

Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees [PDF]

Mathematics, 2021
For a simple graph G=(V,E) with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 if f(v)=1; and (iii) every vertex v with f(v ...
Xinyue Liu, Huiqin Jiang, Pu Wu, Zehui Shao   +3 more
doaj   +2 more sources

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

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 ...
Guoliang Hao, Zhihong Xie, Seyed Mahmoud Sheikholeslami, M. Hajjari   +3 more
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Dominating the Direct Product of Two Graphs through Total Roman Strategies [PDF]

Mathematics, 2020
Given a graph G without isolated vertices, a total Roman dominating function for G is a function f:V(G)→{0,1,2} such that every vertex u with f(u)=0 is adjacent to a vertex v with f(v)=2, and the set of vertices with positive labels induces a graph of ...
Abel Cabrera Martínez, Dorota Kuziak, Iztok Peterin, Ismael G. Yero   +3 more
doaj   +3 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   +2 more sources

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

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
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Quasi-total Roman reinforcement in graphs [PDF]

AKCE International Journal of Graphs and Combinatorics, 2023
A quasi-total Roman dominating function (QTRD-function) on [Formula: see text] is a function [Formula: see text] such that (i) every vertex x for which f(x) = 0 is adjacent to at least one vertex v for which f(v) = 2, and (ii) if x is an isolated vertex ...
N. Ebrahimi, J. Amjadi, M. Chellali, S.M. Sheikholeslami   +3 more
doaj   +2 more sources

Total Roman Reinforcement in Graphs [PDF]

Discussiones Mathematicae Graph Theory, 2019
A total Roman dominating function on a graph G is a labeling f : V (G) → {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2 and the subgraph of G induced by the set of all vertices of positive weight has no isolated vertex.
Ahangar H. Abdollahzadeh, Amjadi J., Chellali M., Nazari-Moghaddam S., Sheikholeslami S.M.   +4 more
doaj   +2 more sources