Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Edge ideals of some edge-weighted graphs

Guangjun Zhu, Shiya Duan, Yijun Cui, Jiaxin Li

Abstract

This paper presents exact formulas for the regularity and depth of powers of edge ideals of an edge-weighted star graph. Additionally, we provide exact formulas for the regularity of powers of the edge ideal of an edge-weighted integrally closed path, as well as lower bounds on the depth of powers of such an edge ideal.

Edge ideals of some edge-weighted graphs

Abstract

This paper presents exact formulas for the regularity and depth of powers of edge ideals of an edge-weighted star graph. Additionally, we provide exact formulas for the regularity of powers of the edge ideal of an edge-weighted integrally closed path, as well as lower bounds on the depth of powers of such an edge ideal.
Paper Structure (6 sections, 23 theorems, 65 equations)

This paper contains 6 sections, 23 theorems, 65 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notions of simple graphs
  4. Notions from commutative algebra
  5. Star graph
  6. path graph

Key Result

Corollary 2.2

If $I=J+K$ is a Betti splitting ideal, then

Theorems & Definitions (44)

  • Definition 2.1
  • Corollary 2.2
  • Lemma 2.3
  • Lemma 2.4
  • Lemma 2.5
  • Lemma 2.6
  • Theorem 3.1
  • proof
  • Lemma 3.2
  • proof
  • ...and 34 more