On a total graph associated to a commutative ring

Let R be a commutative ring with nonzero identity and H be a nonempty proper subset of R such that R/H is a saturated multiplicatively closed subset of R. The generalized total graph of R is the (simple) graph GH(R) with all elements of R as the vertices,and two distinct vertices x and y are adjacent if and only there exist positive integers m and n such that xm+yn E H . In this paper, we investigate the structure of GH(R) .

Keywords:

Total graph , saturated multiplicatively closed