Hodge, Kira2025-04-072025-04-072025https://hdl.handle.net/1828/21746Software has been used in graph theory research for decades, primarily for creating, editing, and analyzing graphs. However, in 2021, Wagner introduced a new approach that uses software to disprove conjectures in graph theory by constructing counterexamples with reinforcement learning. The first goal of this project is to understand Wagner’s deep cross-entropy method. The next goal is to apply this algorithm to more recent conjectures in combinatorics including Brouwer’s Conjecture (2006), which proposes an upper bound on an eigenvalue-related graph parameter. This requires modifying the reward function to encourage the agent to find graphs that exceed the conjectured bound. Further refinements aim to improve the algorithm’s stability and efficiency.engraph theoryreinforcement learningdeep cross-entropy methodcounterexampleslaplacian spectrumPoster