Fuzzy fractional coloring of fuzzy graph with its application

Mahapatra, Tanmoy; Ghorai, Ganesh; Pal, Madhumangal

doi:10.1007/s12652-020-01953-9

Cited by 31 publications

(15 citation statements)

References 28 publications

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“…Akram et al concentrated on a few properties of the edge of m-polar fuzzy graph [2]. Next, Mahapatra and Pal also worked on m-polar fuzzy graph [18,21] and recently, Mahapatra et al studied fuzzy fractional coloring on a fuzzy graph and its generalized topic [19,20]. For more terminologies and applications, see [25].…”

Section: Literature Reviewmentioning

confidence: 99%

An investigation on m-polar fuzzy tolerance graph and its application

Mahapatra

Pal

2021

Neural Comput & Applic

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The tolerance graph is a well-defined topic for a crisp graph theory. But, tolerance in a fuzzy graph is defined recently and many properties have been investigated. But, in a fuzzy graph, only one tolerance is considered for every vertex. But, in an m-polar fuzzy graph (mPFG), each vertex and edge has a m number of membership values. So, defining tolerance for mPFG is not easy and needs some new ideas. By considering m tolerances for every component out of m components of membership values of a vertex or edge, we defined m-polar fuzzy tolerance graph (mPFTG). Here, m-polar fuzzy convex set (mPFCS) as well as strongly mPFCS are also studied. Some different types of mPFTGs like m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also introduced. Some related terms like bounded mPFTG, m-polar fuzzy interval containment graph, m-polar fuzzy unit tolerance graph (mPF unit TG) are also defined. Here, m-polar fuzzy intersection graph along with tolerance core as well as tolerance support length are also discussed. Some interesting properties on m-polar fuzzy min-tolerance graph, m-polar fuzzy max-tolerance graph, m-polar fuzzy sum-tolerance graph are also investigated. Lastly, a real-life application based on an assigned work done by a private company has been discussed to show its practicability in mPFTG.

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Section: Literature Reviewmentioning

confidence: 99%

An investigation on m-polar fuzzy tolerance graph and its application

Mahapatra

Pal

2021

Neural Comput & Applic

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“…Akram et al concentrated a few properties of edge on mPFG [2]. Next, Mahapatra and Pal presented fuzzy colouring of mPFG [11] and recently, Mahapatra et al studied fuzzy fractional colouring on fuzzy graph [12].…”

Section: Research Background and Related Workmentioning

confidence: 99%

An Investigation on M-Polar Fuzzy Saturation Graph and Its Application

Mahapatra

Pal

2021

Preprint

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The saturation graph is a well-defined topic. But, saturation in a fuzzy graph was de ned recently and investigated many properties. In a fuzzy saturation graph, only one saturation is considered for every vertex. In a m-polar fuzzy graph (mPFG), each vertex and edge has a m number of membership values. So, defining saturation for mPFG is not easy and needs some new ideas. By considering m saturation for each component out of m components of membership values of a vertex, we defined saturation in mPFG. α-saturation as well as β-saturation in mPFG is introduced here. Many interesting properties of it are also presented. α-vertex count and β-vertex count in mPFG are also studied and the upper bound on some well known mPFG is also found here. Finally, a real-life application using saturation in mPFG is also presented.

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“…Cyberspace can be expressed mathematically using graph theory since the basic structure of a graph is applicable to the interconnected world of computer networks. Nodes can be associated with various types of hardware or virtual systems as well as routers and other internet infrastructure, and edges can represent connections or information flow between nodes (Mahapatra et al 2020;Dawood 2014). In cybersecurity, a graph-based approach can benefit security operations teams to increase performance and capability by establishing a system of record and intelligence used to inform future threats (Maida 2018).…”

Section: Introductionmentioning

confidence: 99%

Application of graph domination to defend medical information networks against cyber threats

Angel

2022

J Ambient Intell Human Comput

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The principal and supreme concern in medical information systems is the issue of safe guarding the electronic health records of patients. Defending a health care industry's computer network against attacks on its nodes and links requires placing mobile guards on the nodes of a network. Bloom graph topologies are attractive networks that are potential structures for massively parallel computers. This article focuses on the computation of exact value of the parameters which gives the minimum number of guards required to protect the bloom networks with a linear time algorithm. This research highlights the benefits of locating domination sets in locating the minimum number of detection devices or cyber security employees (mobile guards) to be deployed on the significant servers (nodes) of the bloom's topology (healthcare network) which is essential for securing the network to fight against cyber threats.

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Fuzzy fractional coloring of fuzzy graph with its application

Cited by 31 publications

References 28 publications

An investigation on m-polar fuzzy tolerance graph and its application

An investigation on m-polar fuzzy tolerance graph and its application

An Investigation on M-Polar Fuzzy Saturation Graph and Its Application

Application of graph domination to defend medical information networks against cyber threats

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