Characterizations of zero-divisor graphs of certain rings

Abstract

The aim of this paper is to study zero-divisor graphs of some polarity rings, and certain special rings whose zero-divisor graphs are of tournament. Especially, zero-divisor graphs of polar rings, $J$-polar rings and nil-polar rings are connected. In addition, a ring whose zero-divisor graph is a tournament, must be quasinormal, but the converse is not true.