Vertex maps on graphs – Perron–Frobenius theory

Abstract

The goal of this paper is to describe the connections between Perron–Frobenius theory and vertex maps on graphs. In particular, it is shown how Perron–Frobenius theory gives results about the sets of integers that can arise as periods of periodic orbits, about the concepts of transitivity and topological mixing and about horseshoes and topological entropy.

Keywords:

• graphs
• vertex maps
• Markov matrix
• Perron–Frobenius

AMS Subject Classification:

• 37E15
• 37E25
• 37E45

Disclosure statement

No potential conflict of interest was reported by the author.