Spectral radius and signless Laplacian spectral radius of strongly connected digraphs

被引:20
作者
Hong, Wenxi [1 ]
You, Lihua [1 ]
机构
[1] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
关键词
Digraph; Signless Laplacian; Spectral radius; Clique number; Girth; Vertex connectivity; BOUNDS; NUMBER;
D O I
10.1016/j.laa.2014.05.007
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let D be a strongly connected digraph and A(D) be the adjacency matrix of D. Let diag(D) be the diagonal matrix with outdegrees of the vertices of D and Q (D) = diag(D) + A(D) be the signless Laplacian matrix of D. The spectral radius of Q(D) is called the signless Laplacian spectral radius of D, denoted by q(D). In this paper, we give a sharp bound on q(D) where D has a given outdegree sequence and compare the bound with known bounds. We establish some sharp upper or lower bound on q(D) with some given parameter such as clique number, girth or vertex connectivity, and characterize the extremal graph. In addition, we also determine the unique digraph which achieves the minimum (or maximum), the second minimum (or maximum), the third minimum, the fourth minimum spectral radius and signless Laplacian spectral radius among all strongly connected digraphs, and answer the open problem proposed by Lin and Shu [14]. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码:93 / 113
页数:21
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