<![CDATA[In this paper, we study the Laplacian energy and Seidel energy of the non-coprime graphs for the dihedral group $D_n$, $n \geq 3$, $n = p^r$, where $p$ is prime and $r \in \mathbb{Z}^+$, and the generalized quaternion $Q_{4n}$, $n \geq 2$. The investigation starts by obtaining the spectrum for the graphs and then generalizing the formulae for computing the respective energies. It is shown that the Seidel energy for the non-coprime graph for a dihedral group when $n = 2^r$, $r > 1$, is less than the Laplacian energy for the same graph; this is also true for the generalized quaternion. Furthermore, the Seidel energy for the non-coprime graph for a dihedral group $D_n$ when $n = 2^r$, $r > 1$, is the same as the adjacency energy of the same graph for the same group.]]>
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