Directed Power Graphs Of Non-Coprime Cyclic Group Products

In this paper, we investigate the directed power graph of the direct product of cyclic groups, Zm and Zn where m and n are not relatively prime. We conduct a detailed structural analysis of the graphs G(Zp×p), G(Zp×2p)and G(Zp×p2). Here we are utilizing the algebraic properties of Zn and Zm, where m and n are coprime. The study focuses on how the lack of coprimality influences the connectivity and hierarchical structure of these directed power graphs.