@article{Chalarux2026, 
author = {Tanapat Chalarux and Sayan Panma},
title = {On    t-Cayley hypergraphs of cyclic groups with vertex transitive property on the set of non-injective endomorphisms},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {19031-19045},
keywords = {Cayley graph, hypergraph, t-Cayley hypergraph, vertex-transitive graph, endomorphism, automorphism},
url = {https://www.sciopen.com/article/10.3934/math.2026775},
doi = {10.3934/math.2026775},
abstract = {Hypergraphs provide a powerful framework for modeling polyadic relationships, generalizing classical graph structures.    t-Cayley hypergraphs, a natural extension of Cayley graphs, are inherently vertex-transitive under the automorphism group (       A    u    t  ). However, this vertex-transitivity is not necessarily preserved when replacing        A    u    t   with non-injective endomorphisms (             E      n      d        ′  ). This work investigates the precise conditions under which    t-Cayley hypergraphs of finite cyclic groups retain this property. Our main result establishes that a    t-Cayley hypergraph    H over the cyclic group              Z        n   is              E      n      d        ′  -vertex-transitive if    t divides    n.}
}