# Polynomial-delay generation of functional digraphs up to isomorphism

## TL;DR

This paper presents a polynomial-delay, linear-space algorithm for generating all functional digraphs up to isomorphism, including connected and disconnected cases, useful for combinatorial enumeration and dynamical systems analysis.

## Contribution

It introduces a novel reverse search algorithm for efficiently generating functional digraphs up to isomorphism with polynomial delay and linear space complexity.

## Key findings

- Generates functional digraphs with O(n^2) delay
- Handles both connected and disconnected digraphs
- Operates with linear space complexity

## 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.