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.