@article {IOPORT.06025828,
    author       = {LaGrange, John D.},
    title        = {Boolean rings and reciprocal eigenvalue properties.},
    year         = {2012},
    journal      = {Linear Algebra and its Applications},
    volume       = {436},
    number       = {7},
    issn         = {0024-3795},
    pages        = {1863-1871},
    publisher    = {Elsevier Science Inc. (North-Holland), New York, NY},
    doi          = {10.1016/j.laa.2011.05.042},
    abstract     = {Author's abstract: Let $A$ be the adjacency matrix of the zero-divisor graph $\Gamma (R)$ of a finite commutative ring $R$ containing nonzero zero-divisors. In this paper, it is shown that $\Gamma (R)$ is the zero-divisor graph of a Boolean ring if and only if det$(A)= -1$. Also, $A$ is similar to plus or minus its inverse whenever $R$ is a Boolean ring. As a consequence, it is proved that $\Gamma (R)$ is the zero-divisor graph of a Boolean ring if and only if the set of eigenvalues (including multiplicities) of $\Gamma (R)$ can be partitioned into 2-element subsets of the form $\{\lambda , \pm 1/\lambda \}$. Furthermore, any finite Boolean ring $R$ is characterized by the degree and coefficients of the characteristic polynomial of $A$.},
    reviewer     = {Chen Sheng (Harbin)},
    identifier   = {06025828},
}