The Buchsbaum property of symbolic powers of Stanley–Reisner ideals of dimension 1

Let S be a polynomial ring and I be the Stanley–Reisner ideal of a simplicial complex Δ. The purpose of this paper is investigating the Buchsbaum property of S/I(r) when Δ is pure dimension 1. We shall characterize the Buchsbaumness of S/I(r) in terms of the graphical property of Δ. That is closely related to the characterization of the Cohen–Macaulayness of S/I(r) due to the first author and N.V. Trung.