Abstract

The relationship between edges and vertices is fundamental to graph theory, significantly influencing different graph properties and applications. The topological index is a numerical value calculable by specific techniques and graph properties. Meanwhile, the relative prime coprime graph of a group G for its subgroup H is a graph in which two distinct vertices are adjacent whenever the greatest common divisor of the order of both vertices is equal to one or relative prime and either or both are in H. In this paper, we introduce this definition and describe some properties. Moreover, we also define some reverse topological indices (reverse Harmonic, reverse Randic, reverse SK, reverse SK1, and reverse SK2 indices) for the relatively prime coprime graph. In particular, we describe these reverse degree-based topological indices for newly defined relatively prime coprime graphs based on the order of the elements of the integers modulo group.

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