SPECTRA OF BOOLEAN GRAPHS AND CERTAIN MATRICES OF BINOMIAL COEFFICIENTS

Authors : John D LaGrange

Pages : 78-84

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Publication Date : 2011-06-01

Article Type : Research Paper

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 insert ignore into journalissuearticles values(k − 1); × insert ignore into journalissuearticles values(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.
Keywords : adjacency matrix, zero divisor graph, boolean ring