Set Domination in Fuzzy Graphs Using Strong Arcs

Manjusha, O.T.

doi:10.28919/cpr-pajm/1-9

Cited by 10 publications

(7 citation statements)

References 12 publications

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“…Domination in the join of incidence FGs using strong pairs was defined by Nazeer et al [15]. Notes on domination and strong domination and total domination in FGs were introduced by Manjusha and Sunitha [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

A Novel Domination in Vague Influence Graphs with an Application

Shi,

Cai,

Talebi

et al. 2024

Axioms

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Vague influence graphs (VIGs) are well articulated, useful and practical tools for managing the uncertainty preoccupied in all real-life difficulties where ambiguous facts, figures and explorations are explained. A VIG gives the information about the effect of a vertex on the edge. In this paper, we present the domination concept for VIG. Some issues and results of the domination in vague graphs (VGs) are also developed in VIGs. We defined some basic notions in the VIGs such as the walk, path, strength of In-pair , strong In-pair, In-cut vertex, In-cut pair (CP), complete VIG and strong pair domination number in VIG. Finally, an application of domination in illegal drug trade was introduced.

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Section: Introductionmentioning

confidence: 99%

A Novel Domination in Vague Influence Graphs with an Application

Shi,

Cai,

Talebi

et al. 2024

Axioms

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“…In Fuzzy graphs, Paired domination in fuzzy graphs was used to investigate by Manjusha and Sunitha [23,24] Whitehead and Russel [25] established the cartesian product in graphs, and in two graphs, the cartesian product's dominance number and it's developed the problem in PMU, which Haynes et al [26] described as a graph modelling problem.…”

Section: Introductionmentioning

confidence: 99%

Power Domination in Different Graphs with Applications

Saibavani¹,

Parvathi²

2023

MMEP

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Graph theory has grown in importance in applied mathematics as a result of its wide range of applications and utility. Geometry, algebra, number theory, topology, optimization, and computer science all employ graph theory to solve combinatorial issues. Both graph theory and applications rely on the concept of connectedness. Power domination is a generalization of the optimization method in which measuring devices in the specified field are put at precise spots in electronic and electrical power networks. In mathematics, graphs are used to define networks. The classic vertex cover problem and domination problem in graph theory are strongly related to monitoring an electric power system with as few phase measuring units (PMUs) as possible. If every vertex and every edge in the system are seen using the observation criteria of power system monitoring, a set S is a power dominant set (PDS) of a graph G. Thus, the concept of power domination in Strong and Complete graph is established using theorems and examples.

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“…The importance of the domination concepts and adopted them with fuzzy graph using effective edges (E-edges). When the E-edges are absent in a fuzzy graph, Manjusha and Sunitha , 2019 used strong edges and designed the idea of covering and matching. To analyze the problems with an intuitionistic fuzzy environment, the ideas of covering and matching were introduced in IFG (Sahoo et al.…”

Section: Introductionmentioning

confidence: 99%

“…, 2021 . Manjusha and Sunitha , 2019 designed the theory of matching and covering in fuzzy graph using strong edges when considering the absence of E-edges. Recently, the covering problem in fuzzy graph was studied by Mandal et al.…”

Section: Introductionmentioning

confidence: 99%

Bipolar intuitionistic fuzzy graph based decision-making model to identify flood vulnerable region

Nithyanandham,

Augustin,

Narayanamoorthy

et al. 2023

Environ Sci Pollut Res

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Bipolar intuitionistic fuzzy graphs (BIFG) are an extension of fuzzy graphs that can effectively capture uncertain or imprecise information in various applications. In graph theory, the covering, matching, and domination problems are benchmark concepts applied to various domains. These concepts may not be defined precisely using a crisp graph when the vertices and edges are more uncertain. Therefore, this study defines the covering, matching and domination concepts in bipolar intuitionistic fuzzy graphs (BIFG) using effective edges with certain important results. To define these concepts when the effective edges are absent, some novel approaches are discussed. To illustrate the domination concepts, the applications in disaster management and location selection problems are discussed. Further, a BIFG-based decision-making model is designed to identify the flood-vulnerable zones in Chennai, where the city’s most and least vulnerable zones are identified. From the proposed model, Kodambakkam ( ) is the most susceptible zone in Chennai. Finally, a comparative analysis is done with the existing techniques to show the efficiency of the model.

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Set Domination in Fuzzy Graphs Using Strong Arcs

Cited by 10 publications

References 12 publications

A Novel Domination in Vague Influence Graphs with an Application

A Novel Domination in Vague Influence Graphs with an Application

Power Domination in Different Graphs with Applications

Bipolar intuitionistic fuzzy graph based decision-making model to identify flood vulnerable region

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