English

On monoids of endomorphisms of a cycle graph

Rings and Algebras 2023-10-09 v1

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 wEnd(Cn)wEnd(C_n) and End(Cn)End(C_n) of all weak endomorphisms and all endomorphisms of an undirected cycle graph CnC_n with nn vertices. We also describe Green's relations and regularity of these monoids and calculate their cardinalities.

Keywords

Cite

@article{arxiv.2310.04149,
  title  = {On monoids of endomorphisms of a cycle graph},
  author = {Ilinka Dimitrova and Vítor H. Fernandes and Jörg Koppitz and Teresa M. Quinteiro},
  journal= {arXiv preprint arXiv:2310.04149},
  year   = {2023}
}