Turkish Journal of Mathematics
Abstract
In this paper we consider the monoid $DPC_n$ of all partial isometries of an $n$-cycle graph $C_n$. We show that $DPC_n$ is the submonoid of the monoid of all oriented partial permutations on an $n$-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.
DOI
10.55730/1300-0098.3460
Keywords
Transformations, orientation, partial isometries, cycle graphs, rank, presentations
First Page
1746
Last Page
1760
Recommended Citation
FERNANDES, V. H, & PAULISTA, T (2023). On the monoid of partial isometries of a cycle graph. Turkish Journal of Mathematics 47 (6): 1746-1760. https://doi.org/10.55730/1300-0098.3460
