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We introduce t-closed neighborhood ideal of a graph G as an extension of closed
neighborhood ideal of G. We study some algebraic properties of this ideal like minimal …

Let K be a field and R= K [x 1,…, xn] be a polynomial ring in the variables x 1,…, xn. In this
paper, we introduce two classes of monomial ideals of R, which have the following …

Let R= k [x 1,…, xn], where k is a field. The path ideal (of length t) of a directed graph G is the
monomial ideal, denoted by I t (G), whose generators correspond to the directed paths of …

We consider path ideals associated to special classes of posets such as tree posets and
cycles. We express their property of being sequentially Cohen–Macaulay in terms of the …

In this paper, we introduce the concepts of minimal path cover sets and the index of covering
of a simple graph G, and study the basic properties of these notions. Corresponding to these …

In this short note we prove that the projective dimension of a sequentially Cohen-Macaulay
square-free monomial ideal is equal to the maximal height of its minimal primes (also known …

Let Δ Δ be a simplicial complex on vertex set n n. It is shown that if Δ Δ is complete
intersection, Cohen–Macaulay of codimension 2, Gorenstein of codimension 3, or 2-Cohen …

We classify all complete uniform multipartite hypergraphs with respect to some algebraic
properties, such as being (almost) complete intersection, Gorenstein, level, l-Cohen …

Let G be a simple graph and∆ t (G) be a simplicial complex whose facets correspond to the
paths of length t (t≥ 2) in G. It is shown that∆ t (Cn) is matroid, vertex decomposable …