Volume no :5, Issue no: 1, September (2016)

International Journal of Applied Mathematics and Machine Learning

EIGENVALUES OF CAYLEY GRAPHS ON THE GENERALIZED DICYCLIC GROUP

Author's: Pedro Manuel Dominguez Wade
Pages: [25] - [42]
Received Date: May 2, 2016; Revised July 21, 2016
Submitted by: Ali H. Hakami.
DOI: http://dx.doi.org/10.18642/ijamml_7100121664

Abstract

Let G be a finite group. In this paper, we introduce the notion of quasi-normal Cayley graph on G. We show that the eigenvalues of a quasi-normal Cayley graph can be computed as a sum of irreducible characters and eigenvalues of a Hermitian matrix. Moreover, descriptions are given of the spectrum of some quasi-normal Cayley graphs on the generalized dicyclic group.

Keywords

quasi-normal Cayley graph, eigenvalue, irreducible representation, generalized dicyclic group.