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arXiv · 2508.10653

Integral Cayley graphs over a nonabelian group of order $8n$

Bei Ye·Xiaogang Liu
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Abstract

A graph is called an integral graph when all eigenvalues of its adjacency matrix are integers. We study which Cayley graphs over a nonabelian group $$ T_{8n}=\left\langle a,b\mid a^{2n}=b^8=e,a^n=b^4,b^{-1}ab=a^{-1} \right \rangle $$ are integral graphs. Based on the group representation theory, we first give the irreducible matrix representations and characters of $T_{8n}$. Then we give necessary and sufficient conditions for which Cayley graphs over $T_{8n}$ are integral graphs. As applications, we also characterize some families of connected integral Cayley graphs over $T_{8n}$.

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Bei Ye, Xiaogang Liu. 2025-08-14. Integral Cayley graphs over a nonabelian group of order $8n$. https://arxiv.org/abs/2508.10653

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