@article {16535, title = {On the monoid of partial isometries of a cycle graph}, journal = {Turkish Journal of Mathematics (DOI 10.55730/1300-0098.3460)}, volume = {47}, year = {2023}, pages = {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{\textquoteright}s relations of DPC_n and calculate its cardinality and rank.

}, url = {https://journals.tubitak.gov.tr/math/vol47/iss6/10/}, author = {Fernandes, V{\'\i}tor H. and Paulista, T{\^a}nia} } @article {15860, title = {On the monoid of partial isometries of a finite star graph}, journal = {Communications in Algebra (DOI 10.1080/00927872.2022.2121404; Online 14 Sep 2022)}, volume = {51}, year = {2023}, pages = {1028-1048}, abstract = {

In this paper we consider the monoid DPSn of all partial isometries of a star graph Sn with n vertices. Our main objectives are to determine the rank and to exhibit a presentation of DPSn. We also describe Green{\textquoteright}s relations of DPSn and calculate its cardinal.

}, url = {https://doi.org/10.1080/00927872.2022.2121404}, author = {Fernandes, V{\'\i}tor H. and Paulista, T{\^a}nia} } @article {15880, title = {On the Rank of Monoids of Endomorphisms of a Finite Directed Path}, journal = {Asian-European Journal of Mathematics (DOI 10.1142/S1793557123500699; Online 28 Oct 2022)}, volume = {16}, year = {2023}, pages = {2350069 (13 pages)}, abstract = {

In this paper we consider endomorphisms of a finite directed path from monoid generators perspective. Our main aim is to determine the rank of the monoid wEndP_n of all weak endomorphisms of a directed path with n vertices, which is a submonoid of the widely studied monoid O_n of all order-preserving transformations of a n-chain. Also, we describe the regular elements of wEndP_n and calculate its size and number of idempotents.

}, url = {https://doi.org/10.1142/S1793557123500699}, author = {Fernandes, V{\'\i}tor H. and Paulista, T{\^a}nia} }