2023/10/06 by Dimitrova, Ilinka, Fernandes, Vítor H., Koppitz, Jörg +1
#05C25 #05C38 #20M10 #20M20 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2310.04149
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) and End(Cn) 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.