The generalized total graph of a commutative ring

摘要

Let R be a commutative ring with nonzero identity and H be a nonempty proper subset of R such that RH is a saturated multiplicatively closed subset of R. The generalized total graph of R is the (simple) graph GT_H(R) with all elements of R as the vertices, and two distinct vertices x and y are adjacent if and only if x + y ε H. In this paper, we investigate the structure of GT_H(R).