Regularity of Binomial Edge Ideals of Certain Block Graphs

TL;DR

This paper establishes new bounds and exact formulas for the regularity of binomial edge ideals in specific classes of trees and block graphs, advancing understanding of their algebraic properties.

Contribution

It provides improved lower bounds, sharp upper bounds, and exact regularity formulas for binomial edge ideals of trees and certain block graphs.

Findings

Improved lower bound for trees' regularity

Sharp upper bound for specific block-graphs

Exact regularity formulas for lobsters and other classes

Abstract

We obtain an improved lower bound for the regularity of the binomial edge ideals of trees. We prove an upper bound for the regularity of the binomial edge ideals of certain subclass of block-graphs. As a consequence we obtain sharp upper and lower bounds for the regularity of binomial edge ideals of a class of trees called lobsters. We also obtain precise expressions for the regularities of binomial edge ideals of certain classes of trees and block graphs.