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arXiv · 1606.02184

Integral Cayley Graphs over Dihedral Groups

Lu Lu·Qiongxiang Huang·Xueyi Huang
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Abstract

In this paper, we give a necessary and sufficient condition for the integrality of Cayley graphs over the dihedral group $D_n=\langle a,b\mid a^n=b^2=1,bab=a^{-1}\rangle$. Moreover, we also obtain some simple sufficient conditions for the integrality of Cayley graphs over $D_n$ in terms of the Boolean algebra of $\langle a\rangle$, from which we find infinite classes of integral Cayley graphs over $D_n$. In particular, we completely determine all integral Cayley graphs over the dihedral group $D_p$ for a prime $p$.

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Lu Lu, Qiongxiang Huang, Xueyi Huang. 2016-06-07. Integral Cayley Graphs over Dihedral Groups. https://arxiv.org/abs/1606.02184

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