On vertex connectivity of zero-divisor graphs of finite commutative rings

Abstract

Let R be a finite commutative ring with identity. We study the structure of the zero-divisor graph of R and then determine its vertex connectivity when: (i) R is a local principal ideal ring, and (ii) R is a finite direct product of local principal ideal rings. For such rings R, we also characterize the vertices of minimum degree and the minimum cut-sets of the zero-divisor graph of R.