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 …

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 …

We prove that the regularity of binomial edge ideals of graphs obtained by gluing two graphs
at a free vertex is the sum of the regularity of individual graphs. As a consequence, we …

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 …

Let G be a finite simple graph and I(G) denote the corresponding edge ideal. In this paper,
we prove that, if G is a unicyclic graph, then, for all s≧1, the regularity of I(G)^s is exactly …

In this paper, we study the Castelnuovo–Mumford regularity of powers of edge ideals of
product of graphs. We find new upper bounds for reg (I (G∗ H) s) for various classes of …

We prove two recent conjectures on some upper bounds for the Castelnuovo-Mumford
regularity of the binomial edge ideals of some different classes of graphs. We prove the …

arXiv:1708.06883v3 [math.AC] 2 Jan 2019 Page 1 arXiv:1708.06883v3 [math.AC] 2 Jan 2019
LINEAR POLYNOMIAL FOR THE REGULARITY OF POWERS OF EDGE IDEALS OF VERY …

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 …

Assume that $ G $ is a graph with edge ideal $ I (G) $ and let $ I (G)^{(s)} $ denote the $ s $-
th symbolic power of $ I (G) $. It is proved that for every integer $ s\geq 1$, $${\rm reg}(I …