A graph is called very well-covered if it is unmixed without isolated vertices such that the
cardinality of each minimal vertex cover is half the number of vertices. We first prove that a …

A very well–covered graph is an unmixed graph without isolated vertices such that the
height of its edge ideal is half of the number of vertices. We study these graphs by means of …

A very well-covered graph is an unmixed graph whose covering number is half of the
number of vertices. We construct an explicit minimal free resolution of the cover ideal of a …

Let $ G $ be a graph with $ n $ vertices and $ S=\mathbb {K}[x_1,\dots, x_n] $ be the
polynomial ring in $ n $ variables over a field $\mathbb {K} $. Assume that $ J (G) $ is the …

We show that the co-chordal cover number of a graph 𝐺 gives an upper bound for the
Castelnuovo-Mumford regularity of the associated edge ideal. Several known combinatorial …

In a 2008 paper, the first author and Van Tuyl proved that the regularity of the edge ideal of a
graph G is at most one greater than the matching number of G. In this note, we provide a …

Let G be a graph with n vertices, let S= K x_1,\dots, x_n S= K x 1,⋯, xn be the polynomial ring
in n variables over a field KK and let I (G) denote the edge ideal of G. For every collection …

Let G be a bipartite graph with edge ideal I (G) whose quotient ring R/I (G) is sequentially
Cohen–Macaulay. We prove:(1) the independence complex of G must be vertex …

The-number of a graded ideal, denoted by, is the minimum degree of a polynomial for which
is a prime ideal. Jaramillo and Villarreal (J Combin Theory Ser A 177: 105310, 2021) …

In this paper, we explain the regularity, projective dimension and depth of the edge ideal of
some classes of graphs in terms of invariants of graphs. We show that for a $ C_5 $-free …