STUDY THE INTERPLAY BETWEEN THE STRUCTURE OF RING R AND THE GRAPHS ASSOCIATED

Consider the unified ring R. The simple-intersection graph of R (abbreviated GS (R)) is a new kind of graph related with R that we define in this study. Nonzero ideals of R form the vertices of GS (R), and if two vertices cross, it means that both vertices are nonzero simple ideals. Connectedness, bipartiteness, girth, dominant sets, and other graph features of GS (R) are investigated, as is their relationship to R's algebraic qualities. We also provide an exact method for computing the clique and dominance numbers of GS (R), as well as the exact values for its girth and diameter