Affiliations: [a] Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
| [b] Department of Mathematics, Yazd University, Yazd, Iran
Correspondence:
[*]
Corresponding author. Muhammad Akram, Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan. E-mail: [email protected].
Abstract: A Pythagorean fuzzy soft set, an extension of intuitionistic fuzzy soft set, plays an essential role to handle the vagueness in many real-life problems. We apply this concept to graph theory, and present certain new notions including, perfectly regular Pythagorean fuzzy soft graphs (PFSGs), perfectly edge-regular PFSGs and explore some of their properties. We formulate the notion of perfectly irregular PFSGs, perfectly edge-irregular PFSGs and open neighborhood degree sum
(OˆNDS)
and closed neighborhood degree sum
(CˆNDS)
of PFSGs. Finally, we discuss some decision-making problems of PFSGs.
