HS-splitting fields of abelian mixed cayley graphs

For an n-vertex mixed graph 0 , let RS(0) be the Hermitian-adjacency matrix of the second kind of 0 and ⠂A ( R S , & lambda;) = det ( & lambda;In - RS(0) ) the characteristic polynomial of RS(0). The splitting field of ⠂A (R S, & lambda;) is referred to as the HS-splitting field of 0 . Its extension degree over the rational number field Q is referred to as the HS-algebraic de-gree of 0 , and 0 is said to be HS-integral if all eigenvalues of RS(0) are integers. In this paper, we give explicit expressions for the HS-splitting fields of abelian mixed Cay-ley graphs. In addition, we derive a formula to calculate their corresponding HS-algebraic degrees. Moreover, we characterize all HS-integral abelian mixed Cayley graphs.& COPY; 2023 Elsevier Inc. All rights reserved.