On monoids of endomorphisms of a cycle graph
Ilinka Dimitrova, Vítor Hugo Fernandes, Jörg Koppitz, Teresa M. Quinteiro · Mathematica Slovaca · 2024
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 wEndCn and EndCn of all weak endomorphisms and all endomorphisms of an undirected cycle graph Cn with n vertices. We also describe Green’s relations and regularity of these monoids and calculate their cardinalities.