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Comparative Analysis Of Roman And Inverse Roman Domination Numbers Across Graph Families.
Educational Administration: Theory and PracticeThis research paper delves into the intriguing realm of Roman domination and its inverse counterpart within various graph structures. Initially defining Roman domination as a graph theory concept where vertices are covered by distinct dominating sets ...
J. J. Raji, Dr. S Meenakshi
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2020
This chapter is concerned with the concept Roman domination in graphs, which was introduced in 2004 by Cockayne, Dreyer, S.M. Hedetniemi, and S.T. Hedetniemi based on the strategies for defending the Roman Empire presented by Stewart (Sci Am 281:136–139, 1999) and ReVelle and Rosing (ReVelle CS, Rosing KE, Am Math Mon 107:585–594, 2000).
Nader Jafari Rad +3 more
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This chapter is concerned with the concept Roman domination in graphs, which was introduced in 2004 by Cockayne, Dreyer, S.M. Hedetniemi, and S.T. Hedetniemi based on the strategies for defending the Roman Empire presented by Stewart (Sci Am 281:136–139, 1999) and ReVelle and Rosing (ReVelle CS, Rosing KE, Am Math Mon 107:585–594, 2000).
Nader Jafari Rad +3 more
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Algorithmic Aspects of Outer-Independent Double Roman Domination in Graphs
International Journal of Foundations of Computer ScienceLet [Formula: see text] be graph. For any function [Formula: see text], let [Formula: see text], [Formula: see text]. The function [Formula: see text] is called an outer-independent double Roman dominating function (OIDRDF) if the following conditions ...
Amit Sharma +3 more
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(Independent) Roman Domination Parameterized by Distance to Cluster
International Conference on Combinatorial Optimization and ApplicationsGiven a graph $G=(V,E)$, a function $f:V\to \{0,1,2\}$ is said to be a \emph{Roman Dominating function} (RDF) if for every $v\in V$ with $f(v)=0$, there exists a vertex $u\in N(v)$ such that $f(u)=2$.
Pradeesha Ashok +4 more
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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 in unicyclic graphs [PDF]
Journal of Discrete Mathematical Sciences and Cryptography, 2012 Abstract A Roman dominating function on a graph G = (V, E) is a function f : V → {0, 1, 2} 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. The weight of a Roman dominating function is the value w (f) = ∑ u∈V f(u).
T. N. M. Malini Mai +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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Unique Response Roman Domination: Complexity and Algorithms
Algorithmica, 2023Sumanta Banerjee +2 more
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