Bound for the regularity of binomial edge ideals of cactus graphs

TL;DR

This paper establishes an upper bound for the regularity of binomial edge ideals in cactus graphs, focusing on graphs with blocks that are cycles or cliques, and identifies subclasses that attain this bound.

Contribution

It introduces a new upper bound for the regularity of binomial edge ideals in cactus graphs and characterizes subclasses that reach this bound.

Findings

Upper bound for regularity of binomial edge ideals in cactus graphs.

Identification of subclasses attaining the upper bound.

Abstract

In this article, we obtain an upper bound for the regularity of the binomial edge ideal of a graph whose every block is either a cycle or a clique. As a consequence, we obtain an upper bound for the regularity of binomial edge ideal of a cactus graph. We also identify certain subclass attaining the upper bound.