FORGOTTEN, HARARY, AND SCHULTZ INDEXES OF PRIME COPRIME GRAPHS OF THE MODULO GROUP OF INTEGER NUMBERS

Abstract

Topological indices are fundamental to graph theory as they provide numerical measures that capture the structural characteristics and connectivity patterns of a graph. The objective of this study is to find the general formulas for the Forgotten index, Harary index, and Schultz index of the prime coprime graph derived of the group of integers modulo some positive integer. A prime coprime graph is defined as a graph where any two vertices are adjacent if and only if the greatest common divisor (GCD) of the orders of the two vertices is either 1 or a prime number.