Results 221 to 230 of about 25,954 (258)
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Journal of Combinatorial Optimization, 2021
Let $$G=(V,E)$$ be a graph. A function $$f : V \rightarrow \{0, 1, 2\}$$ is an outer independent Roman dominating function (OIRDF) on a graph G if for every ...
A. Poureidi, M. Ghaznavi, J. Fathali
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Let $$G=(V,E)$$ be a graph. A function $$f : V \rightarrow \{0, 1, 2\}$$ is an outer independent Roman dominating function (OIRDF) on a graph G if for every ...
A. Poureidi, M. Ghaznavi, J. Fathali
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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 (v) = 0 has an in-neighbor u with f (u) = 2.
Guoliang Hao, W. Zhuang, Kangxiu Hu
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Twin signed total Roman domination numbers in digraphs
Asian-European Journal of Mathematics, 2017Let [Formula: see text] be a finite simple digraph with vertex set [Formula: see text] and arc set [Formula: see text]. A twin signed total Roman dominating function (TSTRDF) on the digraph [Formula: see text] is a function [Formula: see text] satisfying the conditions that (i) [Formula: see text] and [Formula: see text] for each [Formula: see text ...
J. Amjadi, M. Soroudi
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Quaestiones Mathematicae, 2015
A set S of vertices is a total dominating set of a graph G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set is the total domination number γt(G). A Roman dominating function on a graph G is a function ƒ : V (G) → {0, 1, 2} satisfying the condition that every vertex u with ƒ(u) = 0 is adjacent to at
Chellali, Mustapha +2 more
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A set S of vertices is a total dominating set of a graph G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set is the total domination number γt(G). A Roman dominating function on a graph G is a function ƒ : V (G) → {0, 1, 2} satisfying the condition that every vertex u with ƒ(u) = 0 is adjacent to at
Chellali, Mustapha +2 more
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Algorithmic Aspects of Outer-Independent Total Roman Domination in Graphs
International Journal of Foundations of Computer Science, 2021For a simple, undirected graph [Formula: see text], a function [Formula: see text] which satisfies the following conditions is called an outer-independent total Roman dominating function (OITRDF) of [Formula: see text] with weight [Formula: see text ...
Amit Sharma, P. V. S. Reddy
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Total double Roman domination numbers in digraphs
Discrete Mathematics, Algorithms and Applications, 2021Let [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, F. Pourhosseini
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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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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 {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 ...
Padamutham Chakradhar +1 more
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A characterization relating domination, semitotal domination and total Roman domination in trees
, 2021Abel Cabrera Martínez +2 more
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