- Citation:
- Fernandes, Vítor H., and Tânia Paulista. "On the monoid of partial isometries of a cycle graph." Turkish Journal of Mathematics (DOI 10.55730/1300-0098.3460). 47 (2023): 1746-1760.

### 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 a 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 cardinality and rank.

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