SPECTRA OF BOOLEAN GRAPHS AND CERTAIN MATRICES OF BINOMIAL COEFFICIENTS

Abstract

Given an integer k > 1, let A be the adjacency matrix of the zero-divisor graph of the finite Boolean ring of order 2k. In this paper, the spectra of two (k − 1) × (k − 1) matrices P and Q of binomial coefficients are shown to be linked to the spectrum of the larger matrix A. Since earlier investigations provide the eigenvalues and eigenvectors of Q, certain eigenvalues and eigenvectors of A are obtained.