Finite automata for testing uniqueness of Eulerian trails

TL;DR

This paper introduces a finite automaton to efficiently determine the uniqueness of Eulerian trails in directed graphs, enabling immediate detection of non-uniqueness without full trail traversal.

Contribution

It presents a novel finite automaton-based algorithm for testing Eulerian trail uniqueness, improving efficiency over previous methods.

Findings

Automaton effectively detects non-uniqueness instantly.

Algorithm reduces computational effort in Eulerian trail analysis.

Provides a new tool for graph trail analysis.

Abstract

We investigate the condition under which the Eulerian trail of a digraph is unique, and design a finite automaton to examine it. The algorithm is effective, for if the condition is violated, it will be noticed immediately without the need to trace through the whole trail.