2025/07/10 by Meiqi Peng, Peng, Meiqi, Yuefeng Yang +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2507.07736
openalex publication_date 2025/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 consider a generalized dicyclic group G and for each subgroup H of G, by giving an appropriate connection set S, we determine each possibility for (α,β) such that H is an (α,β)-regular set of G.