Irregular Pythagorean Neutrosophic Graphs

P. Chellamani; D. Ajay

Authors

P. Chellamani Department of Mathematics, St. Joseph’s College of Engineering, OMR, Chennai – 600119, Tamilnadu, India;
D. Ajay Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur – 635601, Tamilnadu, India;

Keywords:

Pythagorean Neutrosophic set, Irregular, Pythagorean Neutrosophic graphs, Neighbourhood

Abstract

Pythagorean Neutrosophic Fuzzy Graphs integrate the concepts of Pythagorean
neutrosophic sets and graph theory to effectively represent imprecise, inconsistent, and vague
information inherent in many real-world problems. This paper introduces and formalizes the concept
of irregularity in Pythagorean Neutrosophic graphs by defining various classes such as neighbourly
irregular, neighbourly totally irregular, highly irregular, and highly totally irregular Pythagorean
Neutrosophic graphs. The study develops theoretical results related to these irregularities and
provides suitable graphical representations for better understanding. The proposed irregular
Pythagorean Neutrosophic graph models are demonstrated to be significant in areas like pattern
recognition, biological networks, information systems, and other applications involving uncertainty
and vagueness. This work extends the theoretical foundation and practical applicability of
neutrosophic graph theory.

DOI: 10.5281/zenodo.17102826