Well-Covered and Cohen–Macaulay Unitary Cayley Graphs

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Let G(R) be the unitary Cayley graph corresponding to a finite commutative ring R with nonzero identity. Let ΔG(R) be the simplicial complex associated to G(R), whose faces correspond to the independent sets of G(R). We study well-coverednees of G(R) and Cohen–Macaulayness of ΔG(R), i.e., its Stanley–Reisner ring k [ΔG(R)] is a Cohen–Macaulay ring. Furthermore, we show that a unitary Cayley graph is shellable and Gorenstein if it is Cohen–Macaulay.