Some Topological Indices of Order Divisor Graphs of Cyclic Groups

This study investigates order divisor graphs' structural and topological properties derived from cyclic groups. Focusing on the relationship between group order and graph topology, we explore key indices, including the Wiener index, the Harary index, the first Zagreb index, and the second Zagreb index. We use a case-based approach to analyze graphs for cyclic groups of varying orders, from prime powers to more general composite structures. This work extends the theoretical framework of order divisor graphs and provides explicit formulations for their topological indices, highlighting the interplay between algebraic and graph-theoretic properties. These findings contribute to the broader understanding of algebraic graph theory and its applications.