Cohen--Macaulayness of a class of graphs versus the class of their complements

Time: 9:30 - 11:00, March 01, 2023.

Venue: Room 612, A6, Institute of Mathematics, VAST

Abstract: Let $ngeq2$ be an integer. The graph $G(n)$ is obtained by letting all the elements of ${0,ldots,n-1}$ 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 talk, 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. This is a joint work with T. Ashitha, T. Asir, and M. R. Pournaki.