Prime - antimagic labeling of graphs in power management system

Abstract

Prime anti-magic labeling techniques play a vital role in various types of real-world applications in sensor networks, smart city management systems, security models, surveillance systems, and so on. A prime anti-magic technique of graph G is considered as finite, simple, and undirected and also it has p number of vertices and q number of edges. If f is an injection from the vertex set of G to the integers {1, 2, . . . , p} such that for each edge uv, the assignment of adjacent vertices of u and v are relatively prime and the edge induced labeling f(uv) = f(u) + f(v) and hence are all distinct. In this research, some special classes of graphs that admit prime anti-magic technique could play a major role in the water tank power management system.