Structural Properties and Reverse Topological Indices of Order GCD Graphs of Integers Modulo Ring

Romdhini, Mamika Ujianita
Abdurahim, Abdurahim
Maharani, Andika Ellena Saufika Hakim

Journal of the Indonesian Mathematical Society
Vol. 32 No. 2 (2026): JUNE

The order GCD graph of a ring, having the ring elements as the vertex set, and two distinct vertices are adjacent if and only if the greatest common divisor (gcd) of the order of both vertices is equal to the order of the product of these two vertices in the ring. This paper aims to analyze the reverse Sombor, Randić, and Harmonic indices of the order GCD graph where the set of vertices is integers modulo ring elements. The results provide new insights into the mathematical properties of reverse topological indices and their potential applications.