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In this paper, we study the integral Cayley graphs over a non-abelian group$U_{6n}=\langle a,b\mid a^{2n}=b^3=1, a^{-1}ba=b^{-1}\rangle$ of order $6n$. Wegive a necessary and sufficient condition for the integrality of Cayley graphsover $U_{6n}$. We also study relationships between the integrality of Cayleygraphs over $U_{6n}$ and the Boolean algebra of cyclic groups. As applications,we construct some infinite families of connected integral Cayley graphs over$U_{6n}$.

Integral Cayley graphs over a group of order $6n$