Classes of graphs that are not Cohen–Macaulay classes
Year: 2025
Type: article
Abstract: 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 $\mathbb{K}[x_1,\ldots,x_n]/I$ 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.
Authors: T. Asir, T. Ashitha
Institution: Pondicherry University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408972556