A note on watchman's walks in de Bruijn graphs

TL;DR

This paper explores the watchman's walk problem in de Bruijn graphs, linking it to de Bruijn sequences and extending the concept to specific subdigraphs, offering insights into graph domination and sequence construction.

Contribution

It establishes a connection between watchman's walks in de Bruijn graphs and de Bruijn sequences, extending the concept to certain subdigraphs, thus broadening understanding of graph domination.

Findings

Watchman's walk in de Bruijn graphs corresponds to de Bruijn sequences.

Extension of watchman's walk concept to specific subdigraphs.

Insights into minimal closed dominating walks in directed graphs.

Abstract

The watchman's walk problem in a digraph calls for finding a minimum length closed dominating walk, where direction of arcs is respected. The watchman's walk of a de Bruijn graph of order $k$ is described by a de Bruijn sequence of order $k-1$. This idea is extended to certain subdigraphs of de Bruijn graphs.