University of Guilan Journal of Algebra and Related Topics 2345-3931 11 2 2023 12 01 Some results of the minimum edge dominating energy of the Cayley graphs for the finite group Sn 135 148 7433 10.22124/jart.2023.23490.1476 EN Sh. Chokani Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran. F. Movahedi Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran. S. M. Taheri Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran. Journal Article 2022 12 22 ‎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 $S_n$‎. https://jart.guilan.ac.ir/article_7433_8fc804f3dd633f09d00fd007c7b4a22a.pdf