论文标题
在Hermitian邻接矩阵上的混合图
On Hermitian Adjacency Matrices for Mixed Graphs
论文作者
论文摘要
我们研究了Mohar [1]引入的第二类（即N-Matrix）的混合图的光谱（即N-Matrix）。我们扩展了一些结果，并定义了一个新的Hermitian邻接矩阵，与弧相对应的条目从$ u $到$ v $等于$ k $ -th（或第三个）团结根，即$ω= cos（2π/k） + \ \\ textbf {i} \ sin（i} \ sin（2π/k），k {2π/k）对应于无向边缘的条目等于1，否则为0。在本文中，我们表征了混合图及其底层图的合适条件。在第4节中，我们确定了混合图的光谱半径上的尖锐上限，并提供相应的极端图。
We study the spectra of mixed graphs about its Hermitian adjacency matrix of the second kind (i.e. N-matrix) introduced by Mohar [1]. We extend some results and define one new Hermitian adjacency matrix, and the entry corresponding to an arc from $u$ to $v$ is equal to the $k$-th( or the third) root of unity, i.e. $ω = cos(2π/k) + \textbf{i} \ sin(2π/k), k {\geq} 3$; the entry corresponding to an undirected edge is equal to 1, and 0 otherwise. In this paper, we characterize the cospectrality conditions for a mixed graph and its underlying graph. In section 4, we determine a sharp upper bound on the spectral radius of mixed graphs, and provide the corresponding extremal graphs.
