On Neighbourhood Based T 0 , T 1 & T 2 Separation Axioms In Graphs

This paper explores neighborhood-based T 0 , T 1 & T 2 separation axioms in graph theory.These separation axioms classify graphs based on their structural properties concerning vertex neighborhoods.We examine theoretical concepts, provide proofs for various types of graphs and explore the implications of these axioms.The findings contribute to understanding graph connectivity and separation, with potential applications in materials science and network design.