论文标题
HS-Integral和Eisenstein积分正常混合Cayley图
HS-integral and Eisenstein integral normal mixed Cayley graphs
论文作者
论文摘要
如果其第二种的遗传学 - 贴上矩阵的特征值是整数，则据说混合图是HS- \ emph {intemall}。如果其（0，1） - 附加矩阵的特征值是Eisenstein Integers，则称为\ Emph {Eisenstein积分}。我们表征了普通混合Cayley图$ \ text {cay}（γ，s）$的集合$ s $对于任何有限的组$γ$。我们进一步表明，当它是Eisenstein的积分时，正常的混合Cayley图是HS的整合性。本文概括了[M. Kadyan，B。Bhattacharjya。 HS-Integral和Eisenstein积分混合的Cayley图形在Abelian群体上。线性代数应用。 645：68-90，2022]。
A mixed graph is said to be HS-\emph{integral} if the eigenvalues of its Hermitian-adjacency matrix of the second kind are integers. A mixed graph is called \emph{Eisenstein integral} if the eigenvalues of its (0, 1)-adjacency matrix are Eisenstein integers. We characterize the set $S$ for which the normal mixed Cayley graph $\text{Cay}(Γ, S)$ is HS-integral for any finite group $Γ$. We further show that a normal mixed Cayley graph is HS-integral if and only if it is Eisenstein integral. This paper generalizes the results of [M. Kadyan, B. Bhattacharjya. HS-integral and Eisenstein integral mixed Cayley graphs over abelian groups. Linear Algebra Appl. 645:68-90, 2022].
