A V Jayanthan

Let G be a finite simple graph and I(G) denote the corresponding edge ideal. For all s≥ 1 , we obtain upper bounds for reg (I(G) s) for bipartite graphs. We then compare the properties of G and G′, where G′ is the graph associated with the polarization of the ideal (I(G) s+1: e1⋯ es) , where e1, ⋯ , es are edges of G. Using these results, we explicitly compute reg (I(G) s) for several subclasses of bipartite graphs..

In this article, we obtain an improved upper bound for the regularity of binomial edge ideals of trees.

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 generalize certain results of Zafar and Zahid (Electron J Comb 20(4), 2013). We obtain an improved lower bound for the regularity of trees. Further, we characterize trees which attain the lower bound. We prove an upper bound for the regularity of certain subclass of block-graphs. As a consequence, we obtain sharp upper and lower bounds for a class of trees called lobsters.