Automated conjecturing with TxGraffiti

TxGraffiti is a data-driven, heuristic-based computer program developed to automate the process of generating conjectures across various mathematical domains. Since its creation in 2017, TxGraffiti has contributed to numerous mathematical publications, particularly in graph theory. In this paper, we present the design and core principles of TxGraffiti, including its roots in the original Graffiti program, which pioneered the automation of mathematical conjecturing. We describe the data collection process, the generation of plausible conjectures, and methods such as the Dalmatian heuristic for filtering out redundant or transitive conjectures. Additionally, we highlight its contributions to the mathematical literature and introduce a new web-based interface that allows users to explore conjectures interactively. While we focus on graph theory, the techniques demonstrated extend to other areas of mathematics.