Unoriented graphs of monounary algebras

AbstractA problem proposed by G. Birkhoff concerns the relation between finite lattices and unoriented graphs. In the present paper we investigate an analogous problem concerning the relations between monounary algebras and unoriented graphs. To each monounary algebra A we assign in a natural way an unoriented graph G(A) without loops and multiple edges. We describe all monounary algebras B such that G(A) and G(B) are isomorphic. Further, we characterize all monounary algebras A having the property that whenever A1 is a monounary algebra whose unoriented graph G(A1) is isomorphic to G(A), then A1 is isomorphic to A