DOI: 10.2298/fil2602739r ISSN: 0354-5180
Homological invariants of edge ideals of power graphs of finite groups
Bilal Rather, Jianfeng Wang
This article examines the homological invariants, including Castelnuovo-Mumford regularity, projective dimension, and Betti numbers, of the edge ideals associated with the power graphs of integer modulo groups. We characterize the edge ideals of power graphs of group
\mathbb{Z}_{n}
with 2-linear resolution and list all of their Betti numbers. We explicitly determine the projective dimension and extremal Betti numbers of power graphs of
\mathbb{Z}_{n}
. For the power graph of
\mathbb{Z}_{n}
, where n is the product of three distinct primes, the initial graded Betti numbers of its edge ideal are investigated alongside the Hilbert series. We present a general inequality for the Betti numbers and the regularity of edge ideals of power graphs of
\mathbb{Z}_{n}
.