Hyper-Wiener and Harary Indices of The Line Graph of Zero Divisor Graph For Integer Modulo Ring (Jurnal Matematika, Statistika dan Komputasi, 2026)
This paper studies the line graph of the zero divisor graph of the ring Z_(P^n ), where p is a prime and n is a natural number. The main objective is to compute closed formulas for the Hyper–Wiener and Harary indices of the line graph L(〖ΓZ〗_(P^n ) ) and to analyze their relationship with the first Zagreb index of the original graph ΓZ_(P^n ). The results establish connections between structural properties of the zero divisor graph and those of its corresponding line graph, offering a deeper understanding of interactions among degree-based and distance-based topological indices.
Keywords: Line Graph; Zero Divisor Graph; Integer modulo ring; Hyper Wiener index; Harary index; First Zagreb index