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arXiv · 2310.04149

On monoids of endomorphisms of a cycle graph

Ilinka Dimitrova·Vítor H. Fernandes·Jörg Koppitz·Teresa M. Quinteiro
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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.

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Ilinka Dimitrova, Vítor H. Fernandes, Jörg Koppitz, Teresa M. Quinteiro. 2023-10-06. On monoids of endomorphisms of a cycle graph. https://arxiv.org/abs/2310.04149

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