Compressed and partially compressed zero-divisor graphs of finite associative rings

We study some properties of the compressed zero-divisor graph of a finite ring and the partially compressed zero-divisor graph of a finite nilpotent ring. In particular, we describe all nilpotent finite rings whose compressed zero-divisor graphs are some complete graphs with loops. Furthermore, we introduce the notion of partially compressed zero-divisor graph for the nilpotent rings and study the properties of the group. Also, we describe the finite rings whose compressed zero-divisor graph contains a bridge.