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, VITOR H. and PAULISTA, TANIA
(2023)
"On the monoid of partial isometries of a cycle graph,"
Turkish Journal of Mathematics: Vol. 47:
No.
6, Article 10.
https://doi.org/10.55730/1300-0098.3460
Available at:
https://journals.tubitak.gov.tr/math/vol47/iss6/10
