Hyper-Wiener and Harary Indices of The Line Graph of Zero Divisor Graph For Integer Modulo Ring

Fariz Maulana (Universitas Mataram)
I Gede Adhitya Wisnu Wardhana (University of Mataram)

JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI
Vol. 22 No. 3 (2026): May 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.