Vertex N-magic total labeling of Jahangir, Octopus, and cycle-star graphs with applications to chemical reaction networks and water pollution

Abstract

This manuscript investigates Vertex $N$-magic total labellings of two families of graphs: Jahangir graphs $J_{ 2,n}$, Octopus graphs $Oct_n$ for $n \geq 4$ and  Cycle-Star graphs $CS_{3,n}$. This work applies vertex-$N$-magic labeling to chemical reaction networks to ensure stoichiometric balance and conservation of mass, charge, and energy.   Furthermore, I apply this framework to water pollution analysis, where pollutants are modelled as vertices, and their interactions are analyzed through weighted sums.