On monoids of endomorphisms of a cycle graph

Ilinka Dimitrova; Vítor H. Fernandes; Jörg Koppitz; Teresa M. Quinteiro

paper

On monoids of endomorphisms of a cycle graph

arXiv:2310.04149

Abstract

In this paper we consider endomorphisms of an undirected cycle graph from Semigroup Theory perspective. Our main aim is to present a process to determine sets of generators with minimal cardinality for the monoids $w E n d (C_{n})$ and $E n d (C_{n})$ of all weak endomorphisms and all endomorphisms of an undirected cycle graph $C_{n}$ with $n$ vertices. We also describe Green's relations and regularity of these monoids and calculate their cardinalities.