Commutative rings with zero divisor graphs of orders are 23, 24 and 25

Abstract

For a commutative ring with identity 1 0. We denote the set of all zero divisors of  by  and . Let  denote the zero-divisor graph of R. Many authors have investigated zero-divisor graphs of commutative rings. In particular, some authors gave all rings with realizable graph order less than or equal to 22, the exploration of this classification for degrees 23, 24, and 25 is still a subject of ongoing research. In this paper, we present all possible rings when zero divisor graphs order 23, 24 and 25.