Upper Bounds for the Largest Singular Value of Certain Digraph Matrices

被引:0
作者
Stanic, Zoran [1 ]
机构
[1] Univ Belgrade, Fac Math, Studentski Trg 16, Belgrade 11000, Serbia
关键词
Digraph; Oriented graph; (skew) adjacency matrix; Skew Laplacian matrix; Singular value; Eigenvalue; Upper bound; LAPLACIAN SPECTRAL-RADIUS; GRAPHS;
D O I
10.1007/s40840-020-00970-3
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we consider digraphs with possible loops and the particular case of oriented graphs, i.e. loopless digraphs with at most one oriented edge between every pair of vertices. We provide an upper bound for the largest singular value of the skew Laplacian matrix of an oriented graph, the largest singular value of the skew adjacency matrix of an oriented graph and the largest singular value of the adjacency matrix of a digraph. These bounds are expressed in terms of certain parameters related to vertex degrees. We also consider some bounds for the sums of squares of singular values. As an application, for the skew (Laplacian) adjacency matrix of an oriented graph and the adjacency matrix of a digraph, we derive some upper bounds for the spectral radius and the sums of squares of moduli of eigenvalues.
引用
收藏
页码:871 / 879
页数:9
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