Zagreb-Based Indices of Line Graph of Prime Coprime Graph for Integers Modulo Group

Abdurahim (Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Mataram, Mataram, 83125, Indonesia)
Mamika Ujianita Romdhini (Special Interest Group on Graph and Fuzzy Theory (SIGGFT), Faculty of Mathematics and Natural Sciences, University of Mataram, Mataram, 83125, Indonesia)
Jihadil Qudsi (Department of Statistics, Faculty of Mathematics and Natural Sciences, University of Mataram, Mataram, 83125, Indonesia)

Science and Technology Indonesia
Vol. 11 No. 3 (2026): July

In this paper, we investigate the line graph of the prime coprime graph associated with the integers modulo group. Explicit general formulas are derived for the first Zagreb index, the second Zagreb index, and the hyper-Zagreb index of the considered structures. A comparative analysis is performed between the newly obtained results and previously reported findings, highlighting structural differences and index growth behaviour under the line-graph transformation. Furthermore, a statistical analysis is conducted to explore the quantitative relationship between the prime coprime graph and its corresponding line graph with respect to the computed Zagreb-based indices. The results provide deeper insight into the structural complexity of algebraically defined graphs and clarify how degree-based topological descriptors evolve under graph transformations.