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Nordhaus–Gaddum bounds for total Roman domination
Journal of Combinatorial Optimization, 2017In this paper, the authors discuss Nordhaus-Gaddum bounds for the total Roman domination number. In the introductory part, the authors recollect graph preliminaries, open neighborhood, closed neighborhood, degree, complement of a graph, diameter and corona graph. Also, they give Roman dominating function, total Roman dominating function and total Roman
Jafar Amjadi +2 more
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Total Roman domination in digraphs
Quaestiones Mathematicae, 2019Let D be a finite and simple digraph with vertex set V (D). A Roman dominating function (RDF) on a digraph D is a function f : V (D) → {0, 1, 2} satisfying the condition that every vertex v with f ...
Guoliang Hao, Wei Zhuang, Kangxiu Hu
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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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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:
L. Shahbazi +3 more
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Bounds on the signed total Roman 2-domination in graphs
Discrete Mathematics, Algorithms and Applications, 2020Let [Formula: see text] be an integer and [Formula: see text] be a simple and finite graph with vertex set [Formula: see text]. A signed total Roman [Formula: see text]-dominating function (STR[Formula: see text]DF) on a graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex [Formula: see text] with [Formula: see text ...
R. Khoeilar +3 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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