EIGENOF BOOLEAN GRAPHS AND PASCAL-TYPE MATRICES

Authors : John D LAGRANGE

Pages : 109-119

View : 63 | Download : 18

Publication Date : 2013-06-01

Article Type : Research Paper

Abstract :Let R be a commutative ring with 1 6= 0. The zero-divisor graph of R is the insert ignore into journalissuearticles values(undirected); graph whose vertices consist of the nonzero zero-divisors of R such that two distinct vertices x and y are adjacent if and only if xy = 0. Given an integer k > 1, let Ak be the adjacency matrix of the zero-divisor graph of the finite Boolean ring of order 2k. In this paper, it is proved that the eigenvalues of Ak are completely determined by the eigenvalues given by two insert ignore into journalissuearticles values(k − 1); × insert ignore into journalissuearticles values(k − 1); Pascal-type matrices Pk and Qk. Multiplicities are also determined.
Keywords : zero divisor graph, adjacency matrix, Boolean ring

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