Abstract
For an n-vertex mixed graph A, let HS(A) be the Hermitian-adjacency matrix of the second kind of A and ΦA(HS,λ)=det(λIn−HS(A)) the characteristic polynomial of HS(A). The splitting field of ΦA(HS,λ) is referred to as the HS-splitting field of A. Its extension degree over the rational number field Q is referred to as the HS-algebraic degree of A, and A is said to be HS-integral if all eigenvalues of HS(A) are integers. In this paper, we give explicit expressions for the HS-splitting fields of abelian mixed Cayley graphs. In addition, we derive a formula to calculate their corresponding HS-algebraic degrees. Moreover, we characterize all HS-integral abelian mixed Cayley graphs.
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