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arXiv · 2507.07736

Regular sets in Cayley sum graphs on generalized dicyclic groups

Meiqi Peng·Yuefeng Yang
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Abstract

For a graph $\Gamma=(V(\Gamma),E(\Gamma))$, a subset $C$ of $V(\Gamma)$ is called an $(\alpha,\beta)$-regular set in $\Gamma$, if every vertex of $C$ is adjacent to exactly $\alpha$ vertices of $C$ and every vertex of $V(\Gamma)\setminus C$ is adjacent to exactly $\beta$ vertices of $C$. In particular, if $C$ is an $(\alpha,\beta)$-regular set in some Cayley sum graph of a finite group $G$ with connection set $S$, then $C$ is called an $(\alpha,\beta)$-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 $(\alpha,\beta)$ such that $H$ is an $(\alpha,\beta)$-regular set of $G$.

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Meiqi Peng, Yuefeng Yang. 2025-07-10. Regular sets in Cayley sum graphs on generalized dicyclic groups. https://arxiv.org/abs/2507.07736

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