Families of directed graphs and topological conjugacy of the associated Markov-Dyck shifts

TL;DR

This paper investigates the structural properties of strongly connected finite directed graphs that serve as invariants for the topological conjugacy of their associated Markov-Dyck shifts, establishing conditions under which conjugacy implies graph isomorphism.

Contribution

The paper identifies specific structural invariants of directed graphs that determine when topological conjugacy of Markov-Dyck shifts implies graph isomorphism.

Findings

Structural properties are invariants under topological conjugacy.

Conjugacy implies isomorphism for graphs with these properties.

Provides criteria for graph isomorphism based on shift conjugacy.

Abstract

We describe structural properties of strongly connected finite directed graphs, that are invariants of the topological conjugacy of their Markov-Dyck shifts. For strongly connected finite directed graphs with these properties topological conjugacy of their Markov-Dyck shifts implies isomorphism of the graphs.