We study the closed neighborhood ideals and the dominating ideals of graphs, in particular,
some classes of trees and cycles. We prove that the closed neighborhood ideals and the …

In this paper, we first give some sufficient criteria for normality of monomial ideals. As
applications, we show that closed neighborhood ideals of complete bipartite graphs are …

Let I be a square-free monomial ideal in a polynomial ring R= K [x 1,…, xn] over a field K,
𝔪=(x 1,…, xn) be the graded maximal ideal of R, and {u 1,…, u β 1 (I)} be a maximal …

Let I be an ideal in a commutative Noetherian ring R. Then the ideal I has the strong
persistence property if and only if (I k+ 1: RI)= I k for all k, and I has the symbolic strong …

An ideal I in a commutative Noetherian ring R has the strong persistence property if (I t+ 1:
RI)= I t for all positive integers t. In this article, we focus on how some graph operations affect …

We produce a procedure for constructing new normal monomial ideals from other ideals that
are assumed to be normal. This enables us to prove that if the cover ideal of a graph G is …

In this paper, we show that the cover ideals of Jahangir's graphs are normal, and also satisfy
the (symbolic)(strong) persistence property. In addition, we determine when the unique …

In this paper, our main focus is to explore different classes of nearly normally torsion-free
ideals. We first characterize all finite simple connected graphs with nearly normally torsion …

In this paper, we unfold balanced and totally balanced neighborhood hypergraphs to
discover new classes of normally torsion-free monomial ideals. As a consequence, we …

Let R be a commutative Noetherian ring and I be an ideal of R. Then, I has the strong
persistence property if (Ik+ 1: RI)= Ik for all k. Also, we say that I has the symbolic strong …