On the monoid of partial isometries of a cycle graph

Vítor H. Fernandes; Tânia Paulista

On the monoid of partial isometries of a cycle graph

Rings and Algebras 2022-09-01 v2

Authors: Vítor H. Fernandes , Tânia Paulista

Abstract

In this paper we consider the monoid $\DPC_n$ of all partial isometries of a $n$ -cycle graph $C_n$ . We show that $\DPC_n$ is the submonoid of the monoid of all oriented partial permutations on a $n$ -chain whose elements are precisely all restrictions of the dihedral group of order $2n$ . Our main aim is to exhibit a presentation of $\DPC_n$ . We also describe Green's relations of $\DPC_n$ and calculate its cardinal and rank.

Keywords

partial isometries cycle graph monoid presentation green's relations dihedral group

Cite

@article{arxiv.2205.02196,
  title  = {On the monoid of partial isometries of a cycle graph},
  author = {Vítor H. Fernandes and Tânia Paulista},
  journal= {arXiv preprint arXiv:2205.02196},
  year   = {2022}
}

Comments

arXiv admin note: text overlap with arXiv:2203.05504

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