Pythagorean theorem

Planar graph

Combinatorics

Crystal structure

Discrete mathematics

Computer graphics (images)

Graph

Planar

Algebra over a field

Artificial intelligence

Chemistry

Pure mathematics

Isomorphism (crystallography)

Line graph

Geometry

Mathematics

Computer science

Fuzzy logic

Graph isomorphism

Planarity testing

Crystallography

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.

Planar Graphs under Pythagorean Fuzzy Environment