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On the signed total Roman domination and domatic numbers of graphs

Discrete Applied Mathematics, 2016
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Lutz Volkmann
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Signed mixed Roman domination numbers in graphs

Journal of Combinatorial Optimization, 2015
A signed mixed Roman dominating function (SMRDF) on a graph \(G=(V,E)\) is a function \(f:V\cup E\to\{-1,1,2\}\) satisfying the conditions (i) the sum of its function values over any closed mixed neighborhood of an element \(x\in V\cup E\) (the mixed closed neighborhood consists of \(x\) and the elements of \(V\cup E\) adjacent or incident to \(x\)) is
Seyed Mahmoud Sheikholeslami, Lutz Volkmann, H Abdollahzadeh Ahangar   +2 more
exaly   +3 more sources

Signed Roman edge domination numbers in graphs

Journal of Combinatorial Optimization, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Seyed Mahmoud Sheikholeslami, Lutz Volkmann, J Amjadi   +2 more
exaly   +3 more sources

Signed double Roman domination numbers in digraphs

Annals of the University of Craiova - Mathematics and Computer Science Series, 2021
"Let $D=(V,A)$ be a finite simple digraph. A signed double Roman dominating function (SDRD-function) on the digraph $D$ is a function $f:V(D)\rightarrow\{-1,1,2, 3\}$ satisfying the following conditions: (i) $\sum_{x\in N^-[v]}f(x)\ge 1$ for each $v\in V(D)$, where $N^-[v]$ consist of $v$ and all in-neighbors of $v$, and (ii) if $f(v)=-1$, then the ...
Jafar Amjadi, Fatemeh Pourhosseini
openaire   +1 more source

On the signed Roman k-domination in graphs

Quaestiones Mathematicae, 2019
Let k ≥ 1 be an integer and G be a simple and finite graph with vertex set V (G). A signed Roman k-dominating function (SRkDF) on a graph G is a function f : V (G) → {−1, 1, 2} such that (i) every vertex v with f(v) = −1 is adjacent to at least one vertex u with f(u) = 2, (ii) ∑ u∈N[v] f(u) ≥ k holds for any vertex v.
Amjadi, J, Nazari-Moghaddam, S, Sheikholeslami, S.M., Volkmann, L   +3 more
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Roman domination number of signed graphs

2022
Summary: A function \(f:V \rightarrow \{0,1,2\}\) on a signed graph \(S=(G,\sigma)\) where \(G = (V,E)\) is a Roman dominating function (RDF) if \(f(N[v]) = f(v) + \sum_{u \in N(v)} \sigma (uv)f(u) \geq 1\) for all \(v\in V\) and for each vertex \(v\) with \(f(v)=0\) there is a vertex \(u\) in \(N^+(v)\) such that \(f(u) = 2\). The weight of an RDF \(f\
Joseph, James, JOSEPH, MAYAMMA
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The signed Roman domination number of two classes graphs

Discrete Mathematics, Algorithms and Applications, 2020
Let [Formula: see text] be a simple graph with vertex set [Formula: see text] and edge set [Formula: see text]. A signed Roman dominating function (SRDF) of [Formula: see text] is a function [Formula: see text] satisfying the conditions that (i) [Formula: see text] for each [Formula: see text], where [Formula: see text] is the set, called closed ...
Xia Hong 0005, Tianhu Yu, Zhengbang Zha, Huihui Zhang   +3 more
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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

Bounds on the signed total Roman 2-domination in graphs

Discrete Mathematics, Algorithms and Applications, 2020
Let [Formula: see text] be an integer and [Formula: see text] be a simple and finite graph with vertex set [Formula: see text]. A signed total Roman [Formula: see text]-dominating function (STR[Formula: see text]DF) on a graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex [Formula: see text] with [Formula: see text ...
R. Khoeilar, L. Shahbazi, Seyed Mahmoud Sheikholeslami, Zehui Shao   +3 more
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Signed total double Roman k-domination in graphs

Discrete Mathematics, Algorithms and Applications, 2019
A signed total double Roman [Formula: see text]-dominating function (STDRkDF) on an isolated-free graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex [Formula: see text] with [Formula: see text] has at least two neighbors assigned 2 under [Formula: see text] or at least one neighbor [Formula: see text] with [Formula:
L. Shahbazi, Hossein Abdollahzadeh Ahangar, R. Khoeilar, Seyed Mahmoud Sheikholeslami   +3 more
openaire   +2 more sources