Integral Cayley graphs over a nonabelian group of order 8n

2025/08/14 by Ye, Bei, Liu, Xiaogang
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.10653

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=⟨ a,b| a²ⁿ=b⁸=e,aⁿ=b⁴,b^-1ab=a^-1 ⟩ 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.

Citations

• Integral Cayley graphs over a group of order 6n
• Integral Cayley Graphs over Dihedral Groups
• On groups all of whose undirected Cayley graphs of bounded valency are\n integral
• Integral Cayley multigraphs over Abelian and Hamiltonian groups
• New results on the energy of integral circulant graphs

Related

• Integral Cayley graphs over a group of order 6n
• Integral Cayley Graphs over Dihedral Groups
• Integral Cayley graphs and groups
• On groups all of whose undirected Cayley graphs of bounded valency are\n integral
• Integral mixed cayley graph over abelian group