The basis of a significant amount of cryptographic systems for information protection are different computationally hard problems. One of these problems is finding the discrete logarithm value in a certain finite group. The problem is to obtain for any two given elements of this group such natural number that the first element to the power of the number equals the second element.
Commuting graph for a finite group $G$, denoted by $\Gamma_G$, with its set of vertices $G\backslash Z(G)$, where $Z(G)$ is the center of $G$, is a graph with $v_p,v_q \in G \backslash Z(G)$, $v_p \neq v_q$, are adjacent whenever $v_p v_q = v_q v_p$. In recent years, there has been significant research into the energy of graphs, particularly focusing on matrices associated with the degree of vertices. Therefore, motivated by that, our study elaborates on the energy of $\Gamma_G$ for dihedral groups of order $2n$, $D_{2n}$, concerning some graph matrices related to the