关键词: Cayley图, 完美边态转移, 图的谱, 群的表示

Abstract: Let U_6n=〈a,b|a²ⁿ=b³=1, a^-1ba=b^-1〉 be a finite group. By using spectral theory and representation theory of groups, we study the perfect edge state transfer problem of  Cayley graphs over U_6n groups, and characterize  the necessary and sufficient conditions for allowing perfect edge state transfer to occur on Cay(U_6n,S).

Key words: Cayley graph, perfect edge state transfer, spectrum of graph, representation of group