THE HARARY INDEX AND THE GUTMAN INDEX IN POWER GRAPHS WITHIN GROUPS OF PRIME ORDER IN INTEGER MODULO GROUP

This article introduces and defines essential concepts such as the Gutman Index, the Harary Index, and the power graph within the context of integer modulo groups. It highlights Syechan and colleagues' significant contributions and their theorem, demonstrating that the power graph of the integer modulo group becomes a complete graph when the order is prime. Theorems 3.7 and 3.8 further provide formulas for calculating the Harary and Gutman Indices for the power graph of Integer modulo groups, offering valuable insights into the structural properties and connectivity of these mathematical and chemical compounds, ultimately bridging the gap between mathematical theory and practical applications in scientific disciplines.