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

Document Type: Special Issue: Energy of Graphs


Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran


‎‎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 \in 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, ‎are evaluated‎.


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