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Complex Pythagorean fuzzy threshold graphs with application in petroleum replenishment

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Abstract

The purpose of this article is to present a novel idea of complex Pythagorean fuzzy threshold graphs \((\mathcal {CPFTG}_{s})\). We introduce the relation between vertex cardinality and threshold values of a \(\mathcal {CPFTG}\). We propose that \(\mathcal {CPFTG}_{s}\) are free from alternating \(4-cycle\) and these graphs can be built up repeatedly adding an isolated or a dominating vertex. We present that the crisp graph of \(\mathcal {CPFTG}\) is a split graph \((\mathcal {SG})\). Further, the threshold dimension and threshold partition number of \(\mathcal {CPFG}_{s}\) is defined. Some basic results on threshold dimension and threshold partition number also have been discussed. Finally, an application is presented on this developed concept. Due to the wide range of complex Pythagorean fuzzy sets \((\mathcal {CPFS}_{s})\), it is obvious that \(\mathcal {CPFTG}_{s}\) are more helpful and beneficial in modeling a problem as compared to complex fuzzy threshold graphs \((\mathcal {CFTG}_{s})\) and complex intuitionistic fuzzy threshold graphs \((\mathcal {CIFTG}_{s})\).

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, New Campus, P.O. Box No. 54590, Lahore, Pakistan

    Muhammad Akram, Uzma Ahmad &  Rukhsar

  2. Department of Mathematics, Faculty of Sciences, Çankiri Karatekin University, 18100, Çankiri, Turkey

    Faruk Karaaslan

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  1. Muhammad Akram
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  2. Uzma Ahmad
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  3. Rukhsar
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  4. Faruk Karaaslan
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Correspondence to Faruk Karaaslan.

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Akram, M., Ahmad, U., Rukhsar et al. Complex Pythagorean fuzzy threshold graphs with application in petroleum replenishment. J. Appl. Math. Comput. 68, 2125–2150 (2022). https://doi.org/10.1007/s12190-021-01604-y

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