Regular Property on Product of Pythagorean Anti Fuzzy Graph

Abstract

In this paper, we introduce the notion of Pythagorean Anti fuzzy graph. We then define the Cartesian product and Lexicographic product on Pythagorean Anti fuzzy graph. It is proved that Cartesian product of two Pythagorean Anti fuzzy graphs is Pythagorean Anti fuzzy graph and Lexicographic product of two Pythagorean Anti fuzzy graphs is Pythagorean Anti fuzzy graph. In general, Cartesian product and lexicographic product of two regular Pythagorean Anti fuzzy graphs need not be Pythagorean Anti fuzzy graph. Necessary and sufficient conditions for Cartesian and lexicographic product of two Pythagorean Anti fuzzy graphs to be regular are determined. Further, we define the concept of isomorphism on Pythagorean Anti fuzzy graph with suitable example.