# The edge ideal of a graph and its splitting graphs

## TL;DR

This paper introduces the concept of graph splitting and compares the algebraic properties of edge ideals between original graphs and their splitting counterparts.

## Contribution

It presents a new concept of graph splitting and analyzes how it affects the algebraic properties of edge ideals.

## Key findings

- Comparison of algebraic properties between graphs and their splitting graphs
- Identification of conditions under which properties are preserved
- New insights into the structure of edge ideals

## Abstract

We introduce and study the concept which we call the splitting of a graph and compare algebraic properties of the edge ideals of graphs and those of their splitting graphs.