On monoids of endomorphisms of a cycle graph

Citation:
Dimitrova, I., Vítor H. Fernandes, J. Koppitz, and T. M. Quinteiro. "On monoids of endomorphisms of a cycle graph." Mathematica Slovaca (DOI 10.1515/ms-2024-0078; Online 15 October 2024). 74.5 (2024): 1071-1088.

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 $wEnd(C_n)$ and $End(C_n)$ 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.

Related External Link

arXiv:

http://arxiv.org/pdf/2310.04149