Characteristic polynomials and spectra of Boolean graphs

Abstract

Three theorems are proved by using fundamental concepts concerned with the eigenvectors and the dimension of the space of eigenvectors and by considering that the Boolean graph Bn is a regular graph of nth degree. The results are discussed by applying these theorems to graphs B 1, B 2, B 3.It is shown that the positive integer nis the greatest eigenvalue of Bn so that multiplicity of n is one and the negative integer — n is the smallest eigenvalue of Bn so that multiplicity of — nis one. Hence, by making a suitable generalization to the spectrums and characteristic polynomials of graphs B 1, B 2, B 3.general formulas are presented related with the discovery of all spectrums and characteristic polynomials of graphs Bn (n ϵ Z+).