Limit points of eigenvalues of (di)graphs

被引：15
作者：
Zhang, Fuji [1 ]
Chen, Zhibo
机构：
[1] Xiamen Univ, Dept Math, Xiamen 361005, Peoples R China
[2] Penn State Univ, Dept Math, Mckeesport, PA 15132 USA
来源：
CZECHOSLOVAK MATHEMATICAL JOURNAL | 2006年 / 56卷 / 03期
基金：
中国国家自然科学基金;
关键词：
limit point; eigenvalue of digraph (graph); double cover; subdivision digraph; line digraph;
D O I：
10.1007/s10587-006-0064-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The study on limit points of eigenvalues of undirected graphs was initiated by A. J. Hoffman in 1972. Now we extend the study to digraphs. We prove: 1. Every real number is a limit point of eigenvalues of graphs. Every complex number is a limit point of eigenvalues of digraphs. 2. For a digraph D, the set of limit points of eigenvalues of iterated subdivision digraphs of D is the unit circle in the complex plane if and only if D has a directed cycle. 3. Every limit point of eigenvalues of a set D of digraphs (graphs) is a limit point of eigenvalues of a set <(D)double over dot> of bipartite digraphs (graphs), where <(D)double over dot> consists of the double covers of the members in D. 4. Every limit point of eigenvalues of a set D of digraphs is a limit point of eigenvalues of line digraphs of the digraphs in D. 5. If M is a limit point of the largest eigenvalues of graphs, then -M is a limit point of the smallest eigenvalues of graphs.
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页码：895 / 902
页数：8
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