Eigenvalues of the Cayley Graph of Some Groups with respect to a Normal Subset

Set X = {M11, M12, M22, M23, M24, Zn, T4n, SD8n, Sz(q), G2(q), V8n}, where M11, M12, M22, M23, M24 are Mathieu groups and Zn, T4n, SD8n, Sz(q), G2(q) and V8n denote the cyclic, dicyclic, semi-dihedral, Suzuki, Ree and a group of order 8n presented by V8n = (a, b | a2n = b4 = e, aba = b−1, ab−1a = b), respectively. In this paper, we compute all eigenvalues of Cay(G, T ), where G ∈ X and T is minimal, second minimal, maximal or second maximal normal subset of G \ {e} with respect to its size. In the case that S is a minimal normal subset of G \ {e}, the summation of the absolute value of eigenvalues, energy of the Cayley graph, is evaluated.