the energy and edge energy of some cayley graphs on the abelian group mathbb{z}_{n}^{4}

Let $g=(v, e)$ be a simple graph such that $lambda_1, ldots, lambda_n$ be the eigenvalues of $g$. the energy of graph $g$ is denoted by $e(g)$ and is defined as $e(g)=sum_{i=1}^{n}|lambda_{i}|$. the edge energy of $g$ is the energy of line graph $g$. in this paper, we investigate the energy and edge energy for two cayley graphs on the abelian group $mathbb{z}_{n}^{4}$, namely, the sudoku graph and the positional sudoku graph. also, we obtain graph energy and edge energy of the complement of these two graphs.