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A novel concept on fermatean Fuzzy threshold graph with its application on covid Mandal Sonia* Government General Degree College, Kharagpur-II, Madpur-721149, West Bengal, India *Email: soniamandal1234@gmail.com
Online Published on 20 February, 2024. Abstract In structuring and designing many problems, a graphical theory is significant. In real-life scenarios, a variety of structural designs can be found with crossings. Modelling vagueness and ambiguity in graphical network problems, numerous graph-theoretical extension ideas are provided. The threshold graph has received a lot of attention. However, the fuzzy threshold graph has recently been established and various properties have been explored. For each edge and vertex in a fuzzy threshold graph, only one threshold is considered. In a Fermatean fuzzy graph, each edge and node has a two-membership value. As a result, creating a threshold graph for a Fermatean fuzzy graph is difficult and requires some new features. In this paper, the Fermatean fuzzy threshold graph (FFTG) and Fermatean fuzzy alternating 4-cycle are defined and certain properties are studied. Fermatean fuzzy threshold graph is an extension of a fuzzy threshold graph. There are also many interesting characteristics of FFTG. The FFTG is also reconstructed interestingly. The important parameters viz. Fermatean threshold partition number and Fermatean threshold dimension are described and studied. It is demonstrated that every Fermatean fuzzy threshold graph can be treated as a Fermatean fuzzy split graph. Lastly, we have given a real-world application of FFTG on an oxygen supply from one state to another in a Covid situation. Top Keywords Fermatean fuzzy graphs, Fermatean fuzzy threshold graph, Fermatean fuzzy threshold dimension, Fermatean fuzzy threshold partition number. Top | |
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