Homological invariants of power graphs of groups

Abstract

In the linear strand of the edge ideals of power graphs of integer modulo group, homological invariants such as Castelnuovo-Mumford regularity, projective dimension, and Betti numbers are addressed. We characterize the edge ideals of Power graphs of $\mathbb{Z}_{n}$ with $2$-linear resolution and present all of their Betti numbers.
We present the projective dimension and extremal Betti numbers of power graphs of $\mathbb{Z}_{n}$.
For $\mathbb{Z}_{n}$, with $n$ being the product of three different primes, the initial gradded Betti numbers are illustrated along with the Hilbert series.
We find a general inequality for the Betti numbers and the regularity of edge ideals of power graphs.