Let R be a commutative ring with non-zero identity and G be a multiplicative subgroup of U(R), where U(R) is the multiplicative group of unit elements of R. Also, suppose that S is a non-empty subset of G such that S=1 Then we define G(R,G, S) to be the graph with vertex set R and two distinct elements x, y R are adjacent if and only if there exists s such that x + sy This graph provides a generalization of the unit and unitary Cayley graphs.

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