Burning Graph Simulator

Overview

Research project at the Illinois Geometry Lab (UIUC Math Department), mentored by Sean English, focused on studying the Burning Number Conjecture through computational methods.

Contributions

• Graph Burning Simulation: Developed a simulator for complex graph burning algorithms using Python, processing graphs with over 500 vertices
• Counterexample Verification: Simulated the graph burning process to verify properties of minimal counterexamples for the Burning Number Conjecture
• Spectral Analysis: Used linear algebra to study the spectrum of graphs, deriving properties related to the conjecture for different graph families

Tech Stack

Python (recursive algorithms, matrix frameworks)

Links

• Full paper: Burning Graphs (PDF) — Illinois Geometry Lab paper with Xianghe Xu, Xinrui Chen, and Haozhen Zheng. Derives bounds on the structure of a minimal counterexample to the Burning Number Conjecture (leaf count and pendant path length in the reduced tree case), introduces the relaxed notion of (k, ℓ)-burnability, and presents the checking algorithm this simulator implements.