A graph X is said to be integral if all eigenvalues of the adjacency matrix A(X)of X are integers.In this paper,the integrality of Cayley graphs X(U6n,S)over U6n=<a,b|a2n=b3=1,a-1 ba=b-1>are discussed,the spectra of X(U6n,S)overU6n are characterized by the relationship between the eigenvalues of group and the characters of graph in the spectral group theory,and necessary and sufficient condition for X(U6n,S)to be the integral graphs are obtained.
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