Open Access

ARTICLE

Pythagorean Neutrosophic Planar Graphs with an Application in Decision-Making

by P. Chellamani^1,2,*, D. Ajay¹, Mohammed M. Al-Shamiri^3,4, Rashad Ismail^3,4

1 Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur, 635601, Tamilnadu, India
2 Department of Mathematics, St. Joseph’s College of Engineering, OMR, Chennai, 600119, Tamilnadu, India
3 Department of Mathematics, Faculty of Science and Arts, King Khalid University, Muhayl Assir, Saudi Arabia
4 Department of Mathematics and Computer, Faculty of Science, Ibb University, Ibb, Yemen

* Corresponding Author: P. Chellamani. Email:

Computers, Materials & Continua 2023, 75(3), 4935-4953. https://doi.org/10.32604/cmc.2023.036321

Received 26 September 2022; Accepted 08 February 2023; Issue published 29 April 2023

Abstract

Graph theory has a significant impact and is crucial in the structure of many real-life situations. To simulate uncertainty and ambiguity, many extensions of graph theoretical notions were created. Planar graphs play a vital role in modelling which has the property of non-crossing edges. Although crossing edges benefit, they have some drawbacks, which paved the way for the introduction of planar graphs. The overall purpose of the study is to contribute to the conceptual development of the Pythagorean Neutrosophic graph. The basic methodology of our research is the incorporation of the analogous concepts of planar graphs in the Pythagorean Neutrosophic graphs. The significant finding of our research is the introduction of Pythagorean Neutrosophic Planar graphs, a conceptual blending of Pythagorean Neutrosophic and Planar graphs. The idea of Pythagorean Neutrosophic multigraphs and dual graphs are also introduced to deal with the ambiguous situations. This paper investigates the Pythagorean Neutrosophic planar values, which form the edges of the Pythagorean neutrosophic graphs. The concept of Pythagorean Neutrosophic dual graphs, isomorphism, co-weak and weak isomorphism have also been explored for Pythagorean Neutrosophic planar graphs. A decision-making algorithm was proposed with a numerical illustration by using the Pythagorean Neutrosophic fuzzy graph.

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Keywords

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