Eigenvalues and Energy of the Cayley Graph of some Groups with respect to a Normal Subset

Maryam Jalali, Rad
2017 Mathematics Interdisciplinary Research   unpublished
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 | a 2n = b 4 = e, aba = b −1 , ab −1 a = 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.
more » ... spect 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.