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Total double Roman domination numbers in digraphs
Discrete Mathematics, Algorithms and Applications, 2021 Let [Formula: see text] be a finite and simple digraph with vertex set [Formula: see text]. A double Roman dominating function (DRDF) on digraph [Formula: see text] is a function [Formula: see text] such that every vertex with label 0 has an in-neighbor with label 3 or two in-neighbors with label 2 and every vertex with label 1 have at least one in ...
Jafar Amjadi, Fatemeh Pourhosseini
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New bounds on the outer-independent total double Roman domination number
Discrete Mathematics, Algorithms and Applications, 2023 A double Roman dominating function (DRDF) on a graph [Formula: see text] is a function [Formula: see text] satisfying (i) if [Formula: see text] then there must be at least two neighbors assigned two under [Formula: see text] or one neighbor [Formula: see text] with [Formula: see text]; and (ii) if [Formula: see text] then [Formula: see text] must be ...
Seyed Mahmoud Sheikholeslami +1 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 +3 more
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Algorithmic Aspects of Total Roman and Total Double Roman Domination in Graphs
, 2021 For a simple, undirected and connected graph \(G = (V, E)\), a total Roman dominating function (TRDF) \(f : V \rightarrow \lbrace 0, 1, 2 \rbrace \) has the property that, every vertex u with \(f(u) = 0\) is adjacent to at least one vertex v for which \(f(v) = 2\) and the subgraph induced by the set of vertices labeled one or two has no isolated ...
Padamutham Chakradhar +1 more
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On computing total double Roman domination number of trees in linear time
, 2020 Let $G=(V,E)$ be a graph. A doubleRoman dominating function (DRDF) on $G$ is a function$f:Vto{0,1,2,3}$ such that for every vertex $vin V$if $f(v)=0$, then either there is a vertex $u$ adjacent to $v$ with $f(u)=3$ orthere are vertices $x$ and $y$ adjacent to $v$ with $f(x)=f(y)=2$ and if $f(v)=1$, then there is a vertex $u$ adjacent to $v$ with$f(u ...
Abolfazl Poureidi
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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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Covering total double Roman domination in graphs
2021Summary: For a graph \(G\) with no isolated vertex, a covering total double Roman dominating function (CTDRD function) \(f\) of \(G\) is a total double Roman dominating function (TDRD function) of \(G\) for which the set \(\{v \in V(G)\mid f(v)\neq 0\}\) is a vertex cover set. The covering total double Roman domination number \(\gamma_{\mathrm{ctdR}}(G)
Teymourzadeh, Atieh, Mojdeh, Doost Ali
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Relating total double Roman domination to 2-independence in trees
, 2020 Jafar Amjadi, Mina Valinavaz
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