Spectral Properties of Coprime Graphs for Dihedral Groups (European Journal of Pure and Applied Mathematics, 2025)
For a finite group G, the coprime graph ΓG of G is defined as the graph with vertex set G, the group itself, and two distinct vertices u, v in ΓG are adjacent if and only if gcd(|u|, |v|) = 1, where |u| is the order of u. This study analyzes the characteristic polynomial of matrices for the dihedral group of order 2n, where n is a power of a prime number. In addition, this paper examines the characteristic polynomial of the matrices for a power of a prime number n. The energy of the graph is also obtained.