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+).
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