论文标题
混合凯利图的分裂场上
Splitting fields of mixed Cayley graphs over abelian groups
论文作者
论文摘要
混合图$γ$的分裂字段$ \ mathbb {sf}（γ）$是$ \ mathbb {q} $的最小场扩展，其中包含$γ$的Hermitian邻接矩阵的所有特征值。扩展度$ [\ MATHBB {sf}（γ）：\ Mathbb {q}] $称为$γ$的代数度。在本文中，我们确定了阿贝尔群体上混合的Cayley图的分裂场和代数度。这概括了[K. Mönius，《循环图光谱的拆分场》，J。Elgebra594（15）（2022）154--169]和[M. Kadyan，B。Bhattacharjya，Abelian群体上的整体混合Cayley图，电子。 J. Combin。 28（4）（2021）\＃p4.46]。
The splitting field $\mathbb{SF}(Γ)$ of a mixed graph $Γ$ is the smallest field extension of $\mathbb{Q}$ which contains all eigenvalues of the Hermitian adjacency matrix of $Γ$. The extension degree $[\mathbb{SF}(Γ):\mathbb{Q}]$ is called the algebraic degree of $Γ$. In this paper, we determine the splitting fields and algebraic degrees of mixed Cayley graphs over abelian groups. This generalizes the main results of [K. Mönius, Splitting fields of spectra of circulant graphs, J. Algebra 594(15) (2022) 154--169] and [M. Kadyan, B. Bhattacharjya, Integral mixed Cayley graphs over abelian groups, Electron. J. Combin. 28(4) (2021) \#P4.46].
