Year: 2025
Type: preprint
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 $T_{8n}$.
Source: arXiv (Cornell University)
Authors: Ye, Bei, Liu, Xiaogang
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979365857
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