SOME RESULTS OF THE MINIMUM EDGE DOMINATING ENERGY OF THE CAYLEY GRAPHS FOR THE FINITE GROUP Sn

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