Krull dimension and regularity of binomial edge ideals of block graphs

TL;DR

This paper establishes a lower bound for the regularity of binomial edge ideals of block graphs, introduces a new family called flower graphs, and provides an efficient algorithm for key algebraic invariants.

Contribution

It introduces flower graphs to analyze Betti numbers and offers a linear time algorithm for computing regularity and Krull dimension of binomial edge ideals of block graphs.

Findings

Computed extremal Betti numbers for flower graphs

Established a lower bound for regularity of block graphs

Developed a linear time algorithm for invariants

Abstract

We give a lower bound for the Castelnuovo-Mumford regularity of binomial edge ideals of block graphs by computing the two distinguished extremal Betti numbers of a new family of block graphs, called flower graphs. Moreover, we present a linear time algorithm to compute the Castelnuovo-Mumford regularity and Krull dimension of binomial edge ideals of block graphs.