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A mixed graph is called \emph{second kind hermitian integral}(or\emph{HS-integral}) if the eigenvalues of its Hermitian-adjacency matrix ofsecond kind are integers. A mixed graph is called \emph{Eisenstein integral} ifthe eigenvalues of its (0, 1)-adjacency matrix are Eisenstein integers. Let$\Gamma$ be an abelian group. We characterize the set $S$ for which a mixedCayley graph $\text{Cay}(\Gamma, S)$ is HS-integral. We also show that a mixedCayley graph is Eisenstein integral if and only if it is HS-integral.

HS-integral and Eisenstein integral mixed Cayley graphs over abelian groups