We introduce a family of squarefree monomial ideals associated to finite simple graphs, whose monomial generators correspond to closed neighborhoods of vertices of the underlying graph. Any such ideal is called the closed neighborhood ideal of the graph. We study some algebraic invariants of these ideals like Castelnuovo–Mumford regularity and projective dimension and present some combinatorial descriptions for these invariants in terms of graph invariants.
"Closed neighborhood ideal of a graph." Rocky Mountain J. Math. 50 (3) 1097 - 1107, June 2020. https://doi.org/10.1216/rmj.2020.50.1097