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 …

In this paper we give upper bounds for the regularity of edge ideal of some classes of graphs
in terms of invariants of graph. We introduce two numbers $ a'(G) $ and $ n (G) $ depending …

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 …

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, 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 finite simple graph and I (G) denote the corresponding edge ideal. In this paper,
we obtain upper bounds for the Castelnuovo-Mumford regularity of I (G) q in terms of certain …

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 …

We provide formulas for the projective dimension and the regularity of edge ideals
associated to vertex weighted rooted forests and oriented cycles. We derive from that exact …

In this paper we introduce the concept of clique disjoint edge sets in graphs. Then, for a
graph G, we define the invariant η (G) as the maximum size of a clique disjoint edge set in G …

Let C be a clutter and let IC/ R be its edge ideal. This is a survey paper on the algebraic and
combinatorial properties of R= IC/and C, respectively. We give a criterion to estimate the …