论文标题
在最大的特征值上，有部分方向
On the largest eigenvalue of a mixed graph with partial orientation
论文作者
论文摘要
令$ g $为连接的图形，让$ t $为$ g $的生成树。 $ g $的部分定向$σ$尊重$ t $是$ g $的边缘的方向，除了$ t $的边缘，与$ g_t^σ$相关的结果图。在本文中，我们证明存在$ g $的部分取向$σ$ a $ t $，因此，$ g_t^σ$的Hermitian邻接矩阵中最大的特征值最多是匹配$ g $的匹配多项式的根源的最大绝对值。
Let $G$ be a connected graph and let $T$ be a spanning tree of $G$. A partial orientation $σ$ of $G$ respect to $T$ is an orientation of the edges of $G$ except those edges of $T$, the resulting graph associated with which is denoted by $G_T^σ$. In this paper we prove that there exists a partial orientation $σ$ of $G$ respect to $T$ such that the largest eigenvalue of the Hermitian adjacency matrix of $G_T^σ$ is at most the largest absolute value of the roots of the matching polynomial of $G$.
