ABSTRACT Let S= K [X 1,…, X n] be the polynomial ring over a field K and G be a simple
graph on {1,…, n}. We take the edge ideal I (G)⊆ S of G and investigate algebraic properties …

The edge ideal of a graph and its splitting graphs Page 1 J CA JOURNAL OF COMMUTATIVE
ALGEBRA Volume 14 (2022), No. 1, 27–35 DOI: 10.1216/jca.2022.14.27 © Rocky Mountain …

We focus our attention on well-covered graphs that are vertex decomposable. We show that
for many known families of these vertex decomposable graphs, the set of shedding vertices …

To every finite simple graph G, we associate the so-called edge ideal I (G), which is a square-
free quadratic monomial ideal generated by the monomials corresponding to the edges of G …

If a simplicial complex Δ Δ is vertex decomposable, then the n-sphere moment angle
complex Z _ Δ^ ∨ (D^ n, S^ n-1) Z Δ∨(D n, S n-1) has the homotopy type of the wedges of …

Combinatorial commutative algebra lies at the intersection of two more established fields,
commutative algebra and combinatorics. In commutative algebra, Cohen-Macaulay and …

Let $\mathbb {Z} _ {n} $ be the ring of integers modulo $ n $. The unitary Cayley graph of
$\mathbb {Z} _ {n} $ is defined as the graph $ G (\mathbb {Z} _ {n}) $ with the vertex set …

Let G be a Cohen–Macaulay very well-covered graph. We prove that the h-vector of the
independence complex of G is precisely the f-vector of a flag complex. Moreover, we show …

There are two motivating questions in [M. Mahmoudi, A. Mousivand, M. Crupi, G. Rinaldo, N.
Terai and S. Yassemi, arXiv: 1006.1087 v1] and [M. Mahmoudi, A. Mousivand, M. Crupi, G …

Let $ G $ be a graph with $ n $ vertices, $ S=\mathbb {K}[x_1,\dots, x_n] $ be the polynomial
ring in $ n $ variables over a field $\mathbb {K} $ and $ I (G) $ denote the edge ideal of $ G …