Integral Cayley graphs over a nonabelian group of order $8n$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908490019110912 |
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| author | Ye, Bei Liu, Xiaogang |
| author_facet | Ye, Bei Liu, Xiaogang |
| contents | 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 $T_{8n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10653 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integral Cayley graphs over a nonabelian group of order $8n$ Ye, Bei Liu, Xiaogang Combinatorics 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 $T_{8n}$. |
| title | Integral Cayley graphs over a nonabelian group of order $8n$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.10653 |