2021/05/11 by Honeycutt, Jacob, Sather-Wagstaff, Keri · 4 citations
#05C69 #05E40 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 13F55 #secondary: 05C05
paper · doi:10.48550/arxiv.2105.05007
We investigate Sharifan and Moradi's closed neighborhood ideal of a finite simple graph, which is a square-free monomial ideal in a polynomial ring over a field. We explicitly describe the minimal irreducible decompositions of these ideals. We also characterize the trees whose closed neighborhood ideals are Cohen-Macaulay; in particular, this property for closed neighborhood ideals of trees is characteristic independent.