Generalized m-Polar Fuzzy Planar Graph and Its Application

Planarity of crisp graphs is a well-established field, whereas planarity within a fuzzy framework has seen recent development and extensive exploration. In an m -polar fuzzy graph ( m PFG), each node and edge is associated with m -components, connected through minimal relationships. However, if on...

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Bibliographic Details
Published in:IEEE access 2023, Vol.11, p.138399-138413
Main Authors: Mondal, Uttam, Mahapatra, Tanmoy, Xin, Qin, Pal, Madhumangal
Format: Article
Language:English
Subjects:
Behavioral sciences
dual of generalized m-polar fuzzy planar graph
fuzzy face
Fuzzy graph
Fuzzy systems
Graph theory
Graphs
Image edge detection
Isomorphism
m-polar fuzzy graph
planarity of generalized m-polar fuzzy graph
Social groups
Social networking (online)
Sustainable development
Uncertainty
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Summary:Planarity of crisp graphs is a well-established field, whereas planarity within a fuzzy framework has seen recent development and extensive exploration. In an m -polar fuzzy graph ( m PFG), each node and edge is associated with m -components, connected through minimal relationships. However, if one desires to incorporate maximum, average, or other intermediate relationships between nodes and edges, the m PFG concept becomes inadequate as in the m -polar fuzzy model, only minimum relation is considered. To address this limitation, a generalized model of m PFG is introduced in this article, allowing for a broader range of relationships to be considered simultaneously. This paper also discusses the properties of generalized m -polar fuzzy environments and generalized m -polar fuzzy graphs ( \text{G}m PFGs), highlighting their isomorphism. Several significant findings and insights are presented in this paper. The article delves into the properties and characteristics of generalized m -polar fuzzy planar graphs ( \text{G}m PFPGs) and explores various intriguing aspects related to them. Additionally, a novel concept of a generalized m -polar fuzzy dual graph ( \text{G}m PFDG) is introduced, derived from \text{G}m PFPGs. The paper establishes a relationship between the dual of a \text{G}m PFG and \text{G}m PFG, examining their properties
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2023.3339220