Developed new functionality for the cayleypy/cayleypy repository by implementing Cayley graph generation for the symmetric group S_n using 3-cycles. Introduced two Python APIs, three_cycles and three_cycles_0ij, enabling researchers to efficiently construct and analyze Cayley graphs within the context of permutation groups and graph theory. Enhanced the codebase with targeted unit tests to ensure correctness and robust handling of edge cases, while also supporting advanced analysis through a diameter-focused commit. Emphasized software development best practices and comprehensive testing, delivering a feature that improves the reliability and research readiness of the library without addressing major bug fixes during this period.