### 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 language | English (US) |
---|---|

Pages (from-to) | 895-902 |

Number of pages | 8 |

Journal | Czechoslovak Mathematical Journal |

Volume | 56 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 2006 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Czechoslovak Mathematical Journal*,

*56*(3), 895-902. https://doi.org/10.1007/s10587-006-0064-y

}

*Czechoslovak Mathematical Journal*, vol. 56, no. 3, pp. 895-902. https://doi.org/10.1007/s10587-006-0064-y

**Limit points of eigenvalues of (di)graphs.** / Zhang, Fuji; Chen, Zhibo.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Limit points of eigenvalues of (di)graphs

AU - Zhang, Fuji

AU - Chen, Zhibo

PY - 2006/9/1

Y1 - 2006/9/1

N2 - 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.

AB - 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.

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U2 - 10.1007/s10587-006-0064-y

DO - 10.1007/s10587-006-0064-y

M3 - Article

AN - SCOPUS:33750494535

VL - 56

SP - 895

EP - 902

JO - Czechoslovak Mathematical Journal

JF - Czechoslovak Mathematical Journal

SN - 0011-4642

IS - 3

ER -