Some Cohen–Macaulay graphs arising from finite commutative rings.

For a given finite commutative ring R with 1 ≠ 0 , one may associate a graph which is called the total graph of R. This graph has R as the vertex set and its two distinct vertices x and y are adjacent exactly whenever x + y is a zero-divisor of R. In this paper, we give necessary and sufficient conditions for two classes of total graphs to be Cohen–Macaulay. [ABSTRACT FROM AUTHOR]