Next Article in Journal
Implicit Equations of the Henneberg-Type Minimal Surface in the Four-Dimensional Euclidean Space
Previous Article in Journal
Some Properties of the Fuss–Catalan Numbers
Open AccessArticle

Planar Graphs under Pythagorean Fuzzy Environment

1
Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
2
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54590, Pakistan
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(12), 278; https://doi.org/10.3390/math6120278
Received: 18 October 2018 / Revised: 19 November 2018 / Accepted: 21 November 2018 / Published: 25 November 2018
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. View Full-Text
Keywords: Pythagorean fuzzy planar graphs; Pythagorean fuzzy planarity value; Pythagorean fuzzy dual graphs; weak and co-weak isomorphism Pythagorean fuzzy planar graphs; Pythagorean fuzzy planarity value; Pythagorean fuzzy dual graphs; weak and co-weak isomorphism
Show Figures

Figure 1

MDPI and ACS Style

Akram, M.; Mohsan Dar, J.; Farooq, A. Planar Graphs under Pythagorean Fuzzy Environment. Mathematics 2018, 6, 278.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop