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Algorithmic Aspects of Total Roman and Total Double Roman Domination in Graphs
2021For 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 ...
Chakradhar Padamutham +1 more
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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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Signed total double Roman k-domination in graphs
Discrete Mathematics, Algorithms and Applications, 2019A 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:
Shahbazi, L. +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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Algorithmic aspects of total Roman {3}-domination in graphs
Discrete Mathematics, Algorithms and Applications, 2020For a simple, undirected, connected graph [Formula: see text], a function [Formula: see text] which satisfies the following conditions is called a total Roman {3}-dominating function (TR3DF) of [Formula: see text] with weight [Formula: see text]: (C1) For every vertex [Formula: see text] if [Formula: see text], then [Formula: see text] has [Formula ...
Chakradhar, Padamutham +1 more
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Algorithmic aspects of total Roman \(\{2\}\)-domination in graphs
2021Summary: For a simple, undirected, connected graph \(G\), a function \(h : V \rightarrow \{0,1,2\}\) is called a total Roman \(\{2\}\)-dominating function (TR2DF) if for every vertex \(v \in V\) with weight 0, either there exists a vertex \(u\) in \(N_G(v)\) with weight 2, or at least two vertices \(x\), \(y\) in \(N_G(v)\) each with weight 1, and the ...
P, Chakradhar, P, Venkata Subba Reddy
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Signed total Roman domination and domatic numbers in graphs
Applied Mathematics and ComputationYubao Guo, Lutz Volkmann, Yun Wang
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