  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.
