Randic, Sum-Connectivity, and Their Product Energies of Non-Commuting Graph of Dihedral Groups

One of the most extensively studied topics in chemical graph theory is graph energy. In this paper, we examine the non-commuting graph associated with the dihedral groups of order $2n$, for $n \geq 3$. We determine the spectral radius and the corresponding energies arising from the Randic, sum-connectivity, and the product of the Randic and sum-connectivity matrices of this graph. Our results show that all the obtained energies are strongly hypoenergetic. Moreover, it is shown that, in all cases, each energy is exactly equal to twice its corresponding spectral radius.