Regular sets in Cayley sum graphs on generalized dicyclic groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918152059748352 |
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| author | Peng, Meiqi Yang, Yuefeng |
| author_facet | Peng, Meiqi Yang, Yuefeng |
| contents | 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 $V(Γ)\setminus C$ 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 $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07736 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regular sets in Cayley sum graphs on generalized dicyclic groups Peng, Meiqi Yang, Yuefeng Combinatorics 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 $V(Γ)\setminus C$ 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 $G$. |
| title | Regular sets in Cayley sum graphs on generalized dicyclic groups |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.07736 |