On monoids of endomorphisms of a cycle graph
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) 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.
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