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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
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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
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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
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Signed double Roman \(k\)-domination in graphs [PDF]

Australas. J Comb., 2018
Summary: Let \(G=(V,E)\) be a simple and finite graph with vertex set \(V(G)\), and let \(k\geq 1\) be an integer. A signed double Roman \(k\)-dominating function (SDR\(k\)DF) on a graph \(G\) is a function \(f:V(G)\rightarrow \{-1,1,2,3\}\) such that (i) every vertex \(v\) with \(f(v)=-1\) is adjacent to at least two vertices assigned with 2 or to at ...
Jafar Amjadi, Hong Yang, Sakineh Nazari-Moghaddam, Seyed Mahmoud Sheikholeslami, Zehui Shao   +4 more
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Bounds for signed double Roman k-domination in trees

RAIRO - Operations Research, 2019
Let k ≥ 1 be an integer and G be a simple and finite graph with vertex set V(G). A signed double Roman k-dominating function (SDRkDF) on a graph G is a function f:V(G) → {−1,1,2,3} such that (i) every vertex v with f(v) = −1 is adjacent to at least two vertices assigned a 2 or to at least one vertex w with f(w) = 3, (ii) every vertex v with f(v) = 1 is
Hong Yang, Pu Wu, Sakineh Nazari-Moghaddam, Seyed Mahmoud Sheikholeslami, Xiaosong Zhang 0001, Zehui Shao, Yuan Yan Tang   +6 more
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Double Roman Domination: A Survey

Mathematics, 2023
Darja Rupnik Poklukar, Janez Žerovnik
exaly  

On the signed Roman k-domination in graphs

Quaestiones Mathematicae, 2020
S M Sheikholeslami, Lutz Volkmann
exaly  

Double Roman Domination in Digraphs

Bulletin of the Malaysian Mathematical Sciences Society, 2017
Guoliang Hao, Xiaodan Chen, Lutz Volkmann   +2 more
exaly  

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

Journal of Mathematical Sciences and Informatics
Laila Shahbazi, Hossein Abdollahzadeh Ahangar, Rana Khoeilar, Seyed Mahmoud Sheikholeslami   +3 more
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Signed total Roman domination in graphs

Journal of Combinatorial Optimization, 2015
Lutz Volkmann
exaly