Planar Graphs under Pythagorean Fuzzy Environment

Muhammad Akram, Jawaria Mohsan Dar and Adeel Farooq
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Muhammad Akram: Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
Jawaria Mohsan Dar: Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
Adeel Farooq: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54590, Pakistan

Mathematics, 2018, vol. 6, issue 12, 1-28

Abstract: Graph theory plays a substantial role in structuring and designing many problems. A number of structural designs with crossings can be found in real world scenarios. To model the vagueness and uncertainty in graphical network problems, many extensions of graph theoretical ideas are introduced. To deal with such uncertain situations, the present paper proposes the concept of Pythagorean fuzzy multigraphs and Pythagorean fuzzy planar graphs with some of their eminent characteristics by investigating Pythagorean fuzzy planarity value with strong, weak and considerable edges. A close association is developed between Pythagorean fuzzy planar and dual graphs. This paper also includes a brief discussion on non-planar Pythagorean fuzzy graphs and explores the concepts of isomorphism, weak isomorphism and co-weak isomorphism for Pythagorean fuzzy planar graphs. Moreover, it presents a problem that shows applicability of the proposed concept.

Keywords: Pythagorean fuzzy planar graphs; Pythagorean fuzzy planarity value; Pythagorean fuzzy dual graphs; weak and co-weak isomorphism (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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