ONE SIDED ZERO DIVISOR GRAPHS OF RINGS WITH A TOTAL ORDER

In this paper we consider prime graph of R (denoted by PG(R)) of an associative ring R (introduced by Satyanarayana, Syam Prasad and Nagaraju [1]). This short paper is divided into four Sections. Section-1 is devoted for preliminary definitions. In section-2, we constructed Right zero divisor graph of R (denoted by RZDG(R)) where R = the set of all 2×2 matrices over the ring Z_2 of integers modulo 2. In section-3, we proved some equivalent conditions related to one sided zero divisor graphs on rings with certain total order (which is not concern with the binary operations of the ring R) and compared with prime graph. Some related fundamental results were mentioned.