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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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On Total Roman Domination in Graphs
2017A Roman dominating function (RDF) on a graph \(G = (V,E)\) is a function \( f:V \rightarrow \lbrace 0,1,2\rbrace \) satisfying the condition that every vertex u for which \(f(u) = 0\) is adjacent to at least one vertex v for which \(f(v)=2\). A total Roman dominating function on a graph \(G = (V,E)\) is a Roman dominating function \(f : V \rightarrow ...
P. Roushini Leely Pushpam, S. Padmapriea
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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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Algorithmic aspects of quasi-total Roman domination in graphs
2021Summary: For a simple, undirected, connected graph \(G(V,E)\), a function \(f : V(G) \rightarrow \{0,1,2\}\) which satisfies the following conditions is called a quasi-total Roman dominating function (QTRDF) of \(G\) with weight \(f(V(G))= \sum_{v \in V(G)} f(v)\).
P, Venkata Subba Reddy, Vikas, Mangal
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A characterization relating domination, semitotal domination and total Roman domination in trees
2020Summary: A total Roman dominating function on a graph \(G\) is a function \(f: V(G)\rightarrow\{0,1,2\}\) such that for every vertex \(v\in V(G)\) with \(f(v)=0\) there exists a vertex \(u\in V(G)\) adjacent to \(v\) with \(f(u)=2\), and the subgraph induced by the set \(\{x\in V(G): f(x)\geq 1\}\) has no isolated vertices.
Cabrera Martinez, Abel +2 more
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Total Roman {2}-domination in graphs
Quaestiones Mathematicae, 2021Abel Cabrera MartÃnez +2 more
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Total Roman domination in the lexicographic product of graphs
Discrete Applied Mathematics, 2019Dorota Kuziak
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Bounds on weak roman and 2-rainbow domination numbers
Discrete Applied Mathematics, 2014Mustapha Chellali +2 more
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