Some results of the minimum edge dominating energy of the Cayley graphs for the finite group Sn

‎Let $\Gamma$ be a finite group and $S$ be a non-empty subset of $\Gamma$‎. ‎A Cayley graph of the group $\Gamma$‎, ‎denoted by $Cay(\Gamma‎, ‎S)$ is defined as a simple graph that its vertices are the elements of $\Gamma$ and two vertices $u$ and $v$ are adjacent if $uv^{-1} \in \Gamma$. ‎The minimum edge dominating energy of Cayley graph $Cay(\Gamma‎, ‎S)$ is equal to the sum of the absolute values of eigenvalues of the minimum edge dominating matrix of graph $Cay(\Gamma‎, ‎S)$‎. ‎In this paper‎, ‎we estimate the minimum edge dominating energy of the Cayley graphs for the finite group $S_n$‎.