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^{-۱} \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.

Keywords:

Minimum edge dominating energy , eigenvalue , Cayley graph , Finite group