HS-splitting fields of abelian mixed cayley graphs

Weijun Liu, Jiaqiu Wang and Yongjiang Wu

Applied Mathematics and Computation, 2023, vol. 456, issue C

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.

Keywords: HS-splitting field; HS-integral mixed Cayley graph; HS-algebraic degree (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:456:y:2023:i:c:s0096300323003119

DOI: 10.1016/j.amc.2023.128142

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