Efficient Algebraic Algorithms for Solving the Longest Path Problem on Specific Graph Classes

This paper presents a novel algebraic approach to efficiently solving the Longest Path Problem (LPP) on specific classes of graphs, including trees, uniform block graphs, block graphs, and directed acyclic graphs (DAGs). The authors introduce algebraic conditions and operations that can identify and approximate the solution in polynomial time, without relying on weight or distance functions or being constrained to undirected graphs.