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 …

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 …

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 …

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 a well-covered graph without isolated vertices such that the
size of its minimal vertex covers is half of the number of vertices. If G is a Cohen–Macaulay …

We characterize unmixed and Cohen-Macaulay edge-weighted edge ideals of very well-
covered graphs. We also provide examples of oriented graphs that have unmixed and non …

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 …

We study minimal free resolutions of edge ideals of bipartite graphs. We associate a directed
graph to a bipartite graph whose edge ideal is unmixed, and give expressions for the …

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 …

In this paper, we deal with very well-covered graphs. We first describe the structure of these
kinds of graphs based on the structure of Cohen–Macaulay very well-covered graphs. As an …