Dominating Ideals and Closed Neighborhood Ideals of Graphs

Nasernejad, Mehrdad; Qureshi, Ayesha Asloob; Bandari, Somayeh; Asli, Musapasaouglu,

doi:10.1007/s00009-022-02107-1

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2022

2024

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Cited by 8 publications

(2 citation statements)

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“…It is shown in [20,Lemma 2.2] that DI(G) is the Alexander dual of NI(G), that is, DI(G) = NI(G) ∨ . In order to find more properties of closed neighborhood ideals and dominating ideals, the reader may refer to [9,14,20].…”

Section: Preliminariesmentioning

confidence: 99%

Classes of normally and nearly normally torsion-free monomial ideals

Nasernejad

Qureshi

Khashyarmanesh

et al. 2022

Communications in Algebra

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Let I ⊂ R = K[x 1 , . . . , x n ] be a square-free monomial ideal, q be a prime monomial ideal in R, h be a square-free monomial in R with supp(h) ∩ (supp(q) ∪ supp(I)) = ∅, and L := I ∩ (q, h). In this paper, we first focus on the associated primes of powers of L and explore the normally torsion-freeness of L. We also give an application on a combinatorial result. Next, we study when a square-free monomial ideal is minimally not normally torsion-free. Particularly, we introduce a class of square-free monomial ideals, which are minimally not normally torsion-free.

show abstract

Section: Preliminariesmentioning

confidence: 99%

Classes of normally and nearly normally torsion-free monomial ideals

Nasernejad

Qureshi

Khashyarmanesh

et al. 2022

Communications in Algebra

View full text Add to dashboard Cite

show abstract

“…After that, in [3], Honeycutt and Sather-Wagstaff probed the Cohen-Macaulay, unmixed, and complete intersection properties of closed neighborhood ideals. Next, in [9,7], the authors concentrated on the normality, strong persistence property, persistence property, and symbolic strong persistence property of closed neighborhood ideals and dominating ideals of some classes of graphs.…”

Section: Introductionmentioning

confidence: 99%