SPECTRA OF BOOLEAN GRAPHS AND CERTAIN MATRICES OF BINOMIAL COEFFICIENTS

Year 2011, Volume: 9 Issue: 9, 78 - 84, 01.06.2011

John D. Lagrange

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.

Keywords

adjacency matrix, zero-divisor graph, boolean ring.