On the monoid of partial isometries of a cycle graph

2022/05/04 by Fernandes, Vítor H., Paulista, Tânia
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2205.02196

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.

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