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THE GENERALIZED TOTAL GRAPH OF A COMMUTATIVE RING

2013
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Journal of Algebra and its Applications
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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 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 ∈ H. In this paper, we investigate the structure of GT H (R).

doi:10.1142/s021949881250212x
fatcat:h6w7odciffb6hdvw7xbrnxe6di