Polynomial-delay generation of functional digraphs up to isomorphism

Abstract

We describe a procedure for the generation of functional digraphs up to isomorphism; these are digraphs with uniform outdegree 1, also called mapping patterns, finite endofunctions, or finite discrete-time dynamical systems. This procedure is based on a reverse search algorithm for the generation of connected functional digraphs, which is then applied as a subroutine for the generation of arbitrary ones. Both algorithms output solutions with $O(n^2)$ delay and require linear space with respect to the number $n$ of vertices.