Classes of graphs that are not Cohen–Macaulay classes - Asir, T.; Ashitha, T. (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 512.5 Characterizations of the classes of Cohen–Macaulay graphs are important because when we characterize one of these classes, then we can decide whether a ring of the form K[x_1,…,x_n]/I is Cohen–Macaulay or not, where I is a square-free monomial ideal. For a given commutative ring R, the total graph of R is a simple graph with R as the vertex set and two distinct vertices x and y are adjacent if x+y is a zero-divisor of R. We find two classes of the total graphs that are not Cohen–Macaulay classes.