Irregular Pythagorean Neutrosophic Graphs

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.