论文标题
有关混合图的第二种Hermitian（Quasi）Laplacian矩阵的未成年人的更多信息
More on minors of Hermitian (quasi-)Laplacian matrix of the second kind for mixed graphs
论文作者
论文摘要
混合图$ m_ {g} $是通过给出$ g $的某些边缘的指示从无定向的简单图$ g $获得的图形，其中$ g $通常称为$ m_ {g} $的基础图。在本文中，我们介绍了第二种$ m_ {g} $的两类发病率矩阵，并讨论了这两个矩阵的决定因素，用于无根混合树和独轮混合图。应用这些结果，我们表征了第二种$ m_ {g} $的Hermitian（Quasi）Laplacian矩阵的各种未成年人的明确表达。此外，我们提供了两个足够的条件，即第二种Hermitian（Quasi）Laplacian矩阵的所有辅助因子的绝对值等于基础图$ G $的跨越树的数量。
A mixed graph $M_{G}$ is the graph obtained from an unoriented simple graph $G$ by giving directions to some edges of $G$, where $G$ is often called the underlying graph of $M_{G}$. In this paper, we introduce two classes of incidence matrices of the second kind of $M_{G}$, and discuss the determinants of these two matrices for rootless mixed trees and unicyclic mixed graphs. Applying these results, we characterize the explicit expressions of various minors for Hermitian (quasi-)Laplacian matrix of the second kind of $M_{G}$. Moreover, we give two sufficient conditions that the absolute values of all the cofactors of Hermitian (quasi-)Laplacian matrix of the second kind are equal to the number of spanning trees of the underlying graph $G$.
