Abstract
Let n≥2 be an integer. The graph G(n) is obtained by letting all the elements of {0,…,n−1} to be the vertices and defining distinct vertices x and y to be adjacent if and only if gcd(x+y,n)=1. In this paper, well-coveredness, Cohen–Macaulayness, vertex-decomposability and Gorensteinness of these graphs and their complements are characterized. These characterizations provide large classes of Cohen–Macaulay and non Cohen–Macaulay graphs.
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