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Relations between the Roman k-domination and Roman domination numbers in graphs
Discrete Mathematics, Algorithms and Applications, 2014Let G = (V, E) be a graph and let k be a positive integer. A Roman k-dominating function ( R k-DF) on G is a function f : V(G) → {0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least k vertices v1, v2, …, vk with f(vi) = 2 for i = 1, 2, …, k.
Ahmed Bouchou+2 more
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Roman Domination in Mycielski Graphs: A Study of Some Graphs and a Heuristic Algorithm
Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü DergisiLet G=(V, E) be a graph. A function f: V→\{0,1,2\}, if ∀u for which f(u)=0 is adjacent to ∃v for which f(v)=2, is called a Roman dominating function, and called in short terms RDF. The weight of an RDF f is f(V)=∑\_(v∈V)f(v).
Derya Dogan Durgun+1 more
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Roman Domination and Double Roman Domination Numbers of Sierpiński Graphs $$S(K_n,t)$$
Bulletin of the Malaysian Mathematical Sciences Society, 2021Different types of domination on the Sierpinski graphs $$S(K_n,t)$$ will be studied in this paper. More precisely, we propose a minimal dominating set for each $$S(K_n,t)$$
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Roman Jakobson: ‘The Dominant’
1997The first three stages of Formalist research have been briefly characterized as follows: (1) analysis of the sound aspects of a literary work; (2) problems of meaning within the framework of poetics; (3) integration of sound and meaning into an inseparable whole.
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Signed Roman domination in digraphs
Journal of Combinatorial Optimization, 2013Let $$D$$D be a finite and simple digraph with vertex set $$V(D)$$V(D) and arc set $$A(D)$$A(D). A signed Roman dominating function (SRDF) on the digraph $$D$$D is a function $$f:V(D)\rightarrow \{-1,1,2\}$$f:V(D)?{-1,1,2} satisfying the conditions that (i) $$\sum _{x\in N^-[v]}f(x)\ge 1$$?x?N-[v]f(x)?1 for each $$v\in V(D)$$v?V(D), where $$N^-[v]$$N ...
Seyed Mahmoud Sheikholeslami+1 more
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Unique Response Roman Domination: Complexity and Algorithms
Algorithmica, 2023Sumanta Banerjee+2 more
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Maximal double Roman domination in graphs
Applied Mathematics and Computation, 2022H. Ahangar+3 more
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2nd INTERNATIONAL CONFERENCE ON COMPUTATIONAL SCIENCES-MODELLING, COMPUTING AND SOFT COMPUTING (CSMCS 2022), 2023
M. Shikhi
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M. Shikhi
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Computing Strong Roman Domination of Trees and Unicyclic Graphs in Linear Time
Bulletin of the Malaysian Mathematical Sciences Society, 2022A. Poureidi+3 more
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Roman domination and independent Roman domination on graphs with maximum degree three
Discrete Applied MathematicsA. Luiz
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