Some properties of the zero divisor graph of a commutative ring

Abstract

Let ( R) be the zero divisor graph for a commutative ring with identity. The k-domination number and the 2-packing number of ( R), where R is an Artinian ring, are computed. k-dominating sets and 2-packing sets for the zero divisor graph of the ring of Gaussian integers modulo n, ( Zn[i]), are constructed. The center, the median, the core, as well as the automorphism group of ( Zn[i]) are determined. Perfect zero divisor graphs ( R) are investigated.