Limit points of eigenvalues of (di)graphs

Fuji Zhang, Zhibo Chen

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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 of bipartite digraphs (graphs), where D 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.

Original languageEnglish (US)
Pages (from-to)895-902
Number of pages8
JournalCzechoslovak Mathematical Journal
Volume56
Issue number3
DOIs
StatePublished - Sep 1 2006

Fingerprint

Limit Point
Digraph
Eigenvalue
Graph in graph theory
Line Digraph
Smallest Eigenvalue
Largest Eigenvalue
Complex number
Unit circle
Subdivision
Undirected Graph
Argand diagram
Cover
If and only if
Cycle

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Zhang, Fuji ; Chen, Zhibo. / Limit points of eigenvalues of (di)graphs. In: Czechoslovak Mathematical Journal. 2006 ; Vol. 56, No. 3. pp. 895-902.
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Limit points of eigenvalues of (di)graphs. / Zhang, Fuji; Chen, Zhibo.

In: Czechoslovak Mathematical Journal, Vol. 56, No. 3, 01.09.2006, p. 895-902.

Research output: Contribution to journalArticle

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