Some more results on fuzzy k-competition graphs

Samanta, Sovan; Pal, Madhumangal; Pal, Anita

doi:10.14569/ijarai.2014.030109

Cited by 17 publications

(6 citation statements)

References 29 publications

(24 reference statements)

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“…( 2016a , b ), Samanta and Pal ( 2011b , 2012b , 2015 , 2016 ) and Samanta et al. ( 2014c , d ). Recently, Samanta and Pal ( 2011a , 2012a , 2013 , 2014a , 2015 ) and Samanta et al.…”

Section: Introductionmentioning

confidence: 94%

A study on vague graphs

et al. 2016

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“…( 2016a , b ), Samanta and Pal ( 2011b , 2012b , 2015 , 2016 ) and Samanta et al. ( 2014c , d ). Recently, Samanta and Pal ( 2011a , 2012a , 2013 , 2014a , 2015 ) and Samanta et al.…”

Section: Introductionmentioning

confidence: 94%

A study on vague graphs

et al. 2016

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“…The idea of intuitionistic fuzzy CG was discussed by Sahoo and Pal (2015). As the time goes, a lot of works have also been done over fuzzy CG which can be found in Isaak et al (1992), Kim et al (1995), Cho et al (2000), Samanta et al (2014Samanta et al ( , 2015, Pramanik et al (2016), Akram and Nasir (2017) and Nasir et al (2017).…”

Section: Research Backgroundmentioning

confidence: 99%

Analysis of the effect of medicines over bacteria based on competition graphs with picture fuzzy environment

Das

Ghorai

2020

Comp. Appl. Math.

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In this study, the concept of picture fuzzy competition graph along with its two subclasses such as picture fuzzy k-competition graphs and p-competition picture fuzzy graphs are introduced. Picture fuzzy competition graph is one of the generalization of competition graph. Several properties of picture fuzzy competition graphs have been investigated. Some new types of picture fuzzy graphs have been introduced like picture fuzzy open neighborhood graph and picture fuzzy closed neighborhood graph. In addition, the relationship between picture fuzzy k-competition graph and picture fuzzy k-neighborhood graph are established. An application of picture fuzzy competition graph in medical science is presented.

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“…Borzooie and Rashmanlou [7][8][9][10][11] analyzed several concepts of VGs. Samanta et al [33][34][35][36][37][38] defined fuzzy competition graphs and some bipolar fuzzy graph results. Shao et al [25,26,[39][40][41] introduced new results in FGs and intuitionistic fuzzy graphs.…”

Section: Introductionmentioning

confidence: 99%

Equitable Domination in Vague Graphs With Application in Medical Sciences

et al. 2021

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Considering all physical, biological, and social systems, fuzzy graph (FG) models serve the elemental processes of all natural and artificial structures. As the indeterminate information is an essential real-life problem, which is mostly uncertain, modeling the problems based on FGs is highly demanding for an expert. Vague graphs (VGs) can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems, in which FGs possibly will not succeed in bringing about satisfactory results. In addition, VGs are a very useful tool to examine many issues such as networking, social systems, geometry, biology, clustering, medical science, and traffic plan. The previous definition restrictions in FGs have made us present new definitions in VGs. A wide range of applications has been attributed to the domination in graph theory for several fields such as facility location problems, school bus routing, modeling biological networks, and coding theory. Concepts from domination also exist in problems involving finding the set of representatives, in monitoring communication and electrical networks, and in land surveying (e.g., minimizing the number of places a surveyor must stand in order to take the height measurement for an entire region). Hence, in this article, we introduce different concepts of dominating, equitable dominating, total equitable dominating, weak (strong) equitable dominating, equitable independent, and perfect dominating sets in VGs and also investigate their properties by some examples. Finally, we present an application in medical sciences to show the importance of domination in VGs.

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Some more results on fuzzy k-competition graphs

Cited by 17 publications

References 29 publications

A study on vague graphs

A study on vague graphs

Analysis of the effect of medicines over bacteria based on competition graphs with picture fuzzy environment

Equitable Domination in Vague Graphs With Application in Medical Sciences

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