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Double Roman Domination: A Survey

Mathematics, 2023
Since 2016, when the first paper of the double Roman domination appeared, the topic has received considerable attention in the literature. We survey known results on double Roman domination and some variations of the double Roman domination, and a list ...
Janez Žerovnik, Darja Rupnik-Poklukar
exaly   +2 more sources

Double Roman domination

Discrete Applied Mathematics, 2016
For a graph G=(V,E), a double Roman dominating function is a function f:V→{0,1,2,3} having the property that if f(v)=0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor with f(w)=3, and if f(v)=1, then vertex v must have ...
Teresa W. Haynes, Stephen Hedetniemi
exaly   +2 more sources

On the signed Roman k-domination in graphs

Quaestiones Mathematicae, 2020
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 ...
Lutz Volkmann, S M Sheikholeslami
exaly   +1 more source

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

Outer independent signed double Roman domination

Journal of Applied Mathematics and Computing, 2021
Seyed Mahmoud Sheikholeslami, H Abdollahzadeh Ahangar   +1 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
openaire   +1 more source

Signed double Roman domination in graphs

Discrete Applied Mathematics, 2019
Hossein Abdollahzadeh Ahangar, Seyed Mahmoud Sheikholeslami   +1 more
exaly  

Double Roman Domination in Digraphs

Bulletin of the Malaysian Mathematical Sciences Society, 2017
Lutz Volkmann, Xiaodan Chen
exaly