FACTOR GRAPH OF NON-COMMUTATIVE RING

In this paper we introduce and investigate the new type of graph called ‘Factor Graph' of non-commutative Ring with non-zero identity. We define the Factor Graph of Ring and for each commutative ring R we associate a simple graph F(R). We investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of G then show that the entire Factor graphs are connected.