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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
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On the Quasi-Total Roman Domination Number of Graphs
Mathematics, 2021 Domination theory is a well-established topic in graph theory, as well as one of the most active research areas. Interest in this area is partly explained by its diversity of applications to real-world problems, such as facility location problems ...
José M Sigarreta +2 more
exaly +3 more sources
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 Haynes, Stephen T Hedetniemi
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Quasi-total Roman Domination in Graphs [PDF]
Results in Mathematics, 2019 [EN] A quasi-total Roman dominating function on a graph G=(V,E) is a function f:V ->{0,1,2}satisfying the following: Every vertex for which u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2, and If x is an isolated vertex in ...
Ismael G Yero +2 more
exaly +2 more sources
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Quasi total double Roman domination in trees
2023Summary: A quasi total double Roman dominating function (QTDRD-function) on a graph \(G=(V(G)\), \(E(G))\) is a function \(f:V(G)\longrightarrow \{0,1,2,3\}\) 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 \(w\) with \(f(w)=3\); (ii) if \(f(v)=1\), then vertex \(v ...
Akhoundi, Maryam +3 more
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Bounds on the quasi-total double Roman domination number in graphs
Discrete Mathematics, Algorithms and ApplicationsA 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 [Formula: see text], then vertex [Formula: see text] must have at least two neighbors assigned 2 under [Formula: see text] or one neighbor [Formula: see text] with [Formula: see text]; (ii) if [
J. Amjadi +4 more
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