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Complex Pythagorean Fuzzy Planar Graphs

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Abstract

In this research work, the notion of complex Pythagorean fuzzy planar graph (CPFPG), an extension of Pythagorean fuzzy planar graph, is presented to study the planarity. The planarity of these graphs is based on the extended range of degree from real to complex plane with unit circle. Here, the ideas of complex Pythagorean fuzzy multigraphs (CPFMGs), complex Pythagorean fuzzy planar graphs (CPFPGs) and some distinguished aspects of these graphs are presented by inspecting the complex Pythagorean fuzzy planarity value using weak and strong edges. A close relation is established between CPFPGs and dual graphs. Discussion about the non-planarity of graphs and the concepts of co-weak isomorphism, isomorphism and weak isomorphism for CPFPGs are also added. Furthermore, an application based on the proposed idea is presented to illustrate the efficiency of given model. The comparison study is also given to validate the consistency and superiority of our model.

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, New Campus, Lahore, 4590, Pakistan

    Muhammad Akram & Ayesha Bashir

  2. Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk, 721636, India

    Sovan Samanta

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  1. Muhammad Akram
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  2. Ayesha Bashir
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  3. Sovan Samanta
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Correspondence to Sovan Samanta.

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Akram, M., Bashir, A. & Samanta, S. Complex Pythagorean Fuzzy Planar Graphs. Int. J. Appl. Comput. Math 6, 58 (2020). https://doi.org/10.1007/s40819-020-00817-2

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