论文标题
混合图的$γ$ - 签名的Laplacian邻接矩阵
The $γ$-Signless Laplacian Adjacency Matrix of Mixed Graphs
论文作者
论文摘要
最近引入了混合图$ x $的$α$ -HERMITIAN邻接矩阵$H_α$。它是对无定向图的邻接矩阵的概括。在本文中，我们考虑了复数数字$α$的特殊情况。这使我们能够定义混合图的入射矩阵。因此，我们定义了线图的概括，以及图形的无符号拉普拉斯邻接矩阵的概括。然后，我们研究了混合图的无价拉普拉斯邻接矩阵的光谱特性。最后，我们表征了混合图的无标识的拉普拉斯邻接矩阵奇数，并且以最大和最低的特征值的弧形和最低特征值给出了弧形和挖掘数量的下部和上限。
The $α$-Hermitian adjacency matrix $H_α$ of a mixed graph $X$ has been recently introduced. It is a generalization of the adjacency matrix of unoriented graphs. In this paper, we consider a special case of the complex number $α$. This enables us to define an incidence matrix of mixed graphs. Consequently, we define a generalization of line graphs as well as a generalization of the signless Laplacian adjacency matrix of graphs. We then study the spectral properties of the signless Laplacian adjacency matrix of a mixed graph. Lastly, we characterize when the signless Laplacian adjacency matrix of a mixed graph is singular and give lower and upper bounds of number of arcs and digons in terms of largest and lowest eigenvalue of the signless Laplacian adjacency matrix.
