@article{Peng2025, 
author = {Meiqi Peng and Yuefeng Yang},
title = {Regular sets in Cayley sum graphs on generalized dicyclic groups},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {30186-30205},
keywords = {regular set, Cayley graph, Cayley sum graph, generalized dicyclic group, dicyclic group},
url = {https://www.sciopen.com/article/10.3934/math.20251326},
doi = {10.3934/math.20251326},
abstract = {For a graph    Γ  =  (  V  (  Γ  )  ,  E  (  Γ  )  ), a subset    C of    V  (  Γ  ) is called an    (  α  ,  β  )-regular set in    Γ, if every vertex of    C is adjacent to exactly    α vertices of    C and every vertex of    V  (  Γ  )  ∖  C is adjacent to exactly    β vertices of    C. In particular, if    C is an    (  α  ,  β  )-regular set in some Cayley sum graph of a finite group    G with connection set    S, then    C is called an    (  α  ,  β  )-regular set of    G. In this paper, we considered a generalized dicyclic group    G and for each subgroup    H of    G, by giving an appropriate connection set    S, we determined each possibility for    (  α  ,  β  ) such that    H is an    (  α  ,  β  )-regular set of    G.}
}