On three types of power graphs of finite loops

This article extends the study of power graphs from finite groups to finite power-associative loops. We explore various types of power graphs, including directed, undirected and enhanced, and establish an algebraic property of finite power-associative loops that guarantees isomorphic power graphs across all three types. Our main theorem generalizes previous theorems in the study of power graphs of finite groups, deepening the understanding of the relationships between the algebraic structures of loops and their corresponding power graphs.