Domination in Products of Fuzzy Graphs

Somasundaram, A.

doi:10.1142/s0218488505003394

Cited by 27 publications

(10 citation statements)

References 6 publications

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“…Somasundaram and Somasundaram discussed domination in fuzzy graphs. They defined domination using effective edges in fuzzy graph [26,27]. Nagoorgani and Chandrasekharan defined domination in fuzzy graphs using strong arcs [18].…”

Section: Introductionmentioning

confidence: 99%

Set Domination in Fuzzy Graphs Using Strong Arcs

Manjusha¹

2022

Pan-Amer. J. Math.

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Set domination in fuzzy graphs is very useful for solving traffic problems during communication in computer networks and travelling networks. In this article, the concept of set domination in fuzzy graphs using strong arcs is introduced. The strong set domination number of complete fuzzy graph and complete bipartite fuzzy graph is determined. It is obtained the properties of the new parameter and related it to some other known domination parameters of fuzzy graphs. An upper bound for the strong set domination number of fuzzy graphs is also obtained.

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Section: Introductionmentioning

confidence: 99%

Set Domination in Fuzzy Graphs Using Strong Arcs

Manjusha¹

2022

Pan-Amer. J. Math.

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“…Somasundaram and Somasundaram [17] presented an outstanding idea of domination in FGs. Somasundaram [18] discussed various types of products such as union, join, composition, and Cartesian product and their domination parameters for FGs. Gani and Ahamed [19] introduced strong and weak domination in FGs.…”

Section: Introductionmentioning

confidence: 99%

Domination of Fuzzy Incidence Graphs with the Algorithm and Application for the Selection of a Medical Lab

Nazeer

Rashid

Guirao

2021

Mathematical Problems in Engineering

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Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), have been recognized as being an effective tool to tackle real-world problems in which vague data and information are essential. Dominating sets (DSs) have multiple applications in diverse areas of life. In wireless networking, DSs are being used to find efficient routes with ad hoc mobile networks. In this paper, we extend the concept of domination of FGs to the FIGs and show some of their important properties. We propose the idea of order, size, and domination in FIGs. Two types of domination, namely, strong fuzzy incidence domination and weak fuzzy incidence domination, for FIGs are discussed. A relationship between strong fuzzy incidence domination and weak fuzzy incidence domination for complete fuzzy incidence graphs (CFIGs) is also introduced. An algorithm to find a fuzzy incidence dominating set (FIDS) and a fuzzy incidence domination number (FIDN) is discussed. Finally, an application of fuzzy incidence domination (FID) is provided to choose the best medical lab among different labs for the conduction of tests for the coronavirus.

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“…In 1962, the idea of domination in graphs was presented by Ore [ 27 ] and Berge [ 7 ], and thereafter concentrated by Cockayne and Hedetniemi [ 10 , 11 ]. Utilizing effective edges Somasundaram [ 35 , 36 ] explored domination in fuzzy graphs. Afterwards, utilizing strong arc segments domination in the fuzzy graph was talked about by Nagoorgani and Chandrasekaran [ 24 ].…”

Section: Introductionmentioning

confidence: 99%

A novel concept of domination in m-polar interval-valued fuzzy graph and its application

Bera

Pal

2021

Neural Comput & Applic

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The concept of domination is one of the most significant topics in graph theory to handle unpredictable phenomena. In this study, an unprecedented idea of domination is introduced in m - polar interval-valued fuzzy graph ( m -PIVFG). Domination number (DN), isolated vertex, total dominating set, independent set of domination on m -PIVFG are discussed. Some algebraic properties of domination on m -PIVFG are investigated. Weak domination, strong domination, split and non-split domination, cototal and global dominating sets on m -PIVFG are investigated with some fundamental hypotheses and models. We explore the concept of domination in m -PIVFG by solving a case study of locating new facilities to handle a catastrophe reaction activity due to the “COVID-19 pandemic” in West Bengal, India. Ultimately, conclusions and avenues of future scopes are placed at the end of this study.

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Domination in Products of Fuzzy Graphs

Abstract: In this paper we discuss several operations on fuzzy graphs such as union, join, composition, Cartesian product and study their domination parameters.

Cited by 27 publications

References 6 publications

Set Domination in Fuzzy Graphs Using Strong Arcs

Set Domination in Fuzzy Graphs Using Strong Arcs

Domination of Fuzzy Incidence Graphs with the Algorithm and Application for the Selection of a Medical Lab

A novel concept of domination in m-polar interval-valued fuzzy graph and its application

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