The Szeged and Wiener indices for coprime graph of dihedral groups

Abstract

The coprime graph is defined as a graph where two distinct vertices are adjacent if and only if the order of both vertices are coprime. The Szeged index is the summation of the products of the number of vertices which are lying closer to x than y and vice versa. Meanwhile, the Wiener index is the half-sum of the distances for all vertices of the graph. In this paper, the Szeged index and the Wiener index of the coprime graph for certain order of dihedral groups are computed. Then, the general form of the Szeged and Wiener indices of the coprime graph for the dihedral groups are determined.