Results 31 to 40 of about 107,030 (250)

Mixed Roman domination and 2-independence in trees

Communications in Combinatorics and Optimization, 2018
Let $G=(V‎, ‎E)$ be a simple graph with vertex set $V$ and edge set $E$‎. ‎A {\em mixed Roman dominating function} (MRDF) of $G$ is a function $f:V\cup E\rightarrow \{0,1,2\}$ satisfying the condition that every element $x\in V\cup E$ for which $f(x)=0 ...
N. Dehgardi
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On the Outer Independent Total Double Roman Domination in Graphs

Mediterranean Journal of Mathematics, 2023
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Abdollahzadeh Ahangar, H., Chellali, Mustapha, Sheikholeslami, Seyed Mahmoud, Valenzuela Tripodoro, Juan Carlos   +3 more
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Outer-independent total Roman domination in graphs

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 G. Yero   +2 more
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Independent Double Roman Domination Stability in Graph

European Journal of Pure and Applied Mathematics
An independent double Roman dominating function (IDRD-function) on a graph $G$ is a function $f :V(G)\to \{0, 1, 2, 3\}$ having the property that (i) if $f(v) = 0$, then the vertex $v$ must have at least two neighbors assigned 2 under $f$ or one neighbor $w$ with $f(w) = 3$, and if $f(v) = 1$, then the vertex $v$ must have at least one neighbor $w ...
Jamil Hamja, Seyed Mahmoud Sheikholeslami, Mina Esmaeeli, null Cris L. Armada, Imelda S. Aniversario   +4 more
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Exploring algorithmic solutions for the Independent Roman Domination problem in graphs

Discrete Applied Mathematics
Given a graph $G=(V,E)$, a function $f:V\to \{0,1,2\}$ is said to be a \emph{Roman Dominating function} if for every $v\in V$ with $f(v)=0$, there exists a vertex $u\in N(v)$ such that $f(u)=2$. A Roman Dominating function $f$ is said to be an \emph{Independent Roman Dominating function} (or IRDF), if $V_1\cup V_2$ forms an independent set, where $V_i=\
Paul, Kaustav, Sharma, Ankit, Pandey, Arti   +2 more
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Outer Independent Double Roman Domination Stability in Graphs

Ars Combinatoria
An outer independent double Roman dominating function (OIDRDF) on a graph G is a function f : V ( G ) → { 0 , 1 , 2 , 3 } having the property that (i) if f ( v ) = 0 , then the vertex v must have at least two neighbors assigned 2 under f or one neighbor w with f ( w ) = 3 , and if f ( v ) = 1 , then the vertex v must have at least one ...
Sheikholeslami, S. M., Esmaeili, M., Volkmann, L.   +2 more
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Independent Roman Domination Number of Graphs

International Journal of Scientific Research in Mathematical and Statistical Sciences, 2018
D.K. Thakkar, S.M. Badiyani
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Further results on independent double roman trees

AKCE International Journal of Graphs and Combinatorics, 2022
A double Roman dominating function (DRDF) on a graph [Formula: see text] is a function [Formula: see text] such that every vertex u with f(u) = 0 is adjacent to at least one vertex assigned a 3 or to at least two vertices assigned a 2, and every vertex v
A. Rahmouni, H. Abdollahzadeh Ahangar, M. Chellali, S. M. Sheikholeslami   +3 more
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On trees with equal Roman domination and outer-independent Roman domination number [PDF]

Communications in Combinatorics and Optimization, 2019
A Roman dominating function (RDF) on a graph $G$ is a function $f : V (G) \to \{0, 1, 2\}$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v) = 2$.
S. Nazari-Moghaddam, S.M. Sheikholeslami
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Roman {2}-Domination Problem in Graphs

Discussiones Mathematicae Graph Theory, 2022
For a graph G = (V, E), a Roman {2}-dominating function (R2DF) f : V → {0, 1, 2} has the property that for every vertex v ∈ V with f(v) = 0, either there exists a neighbor u ∈ N(v), with f(u) = 2, or at least two neighbors x, y ∈ N(v) having f(x) = f(y) =
Chen Hangdi, Lu Changhong
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