| Title:
|
Limit points of eigenvalues of (di)graphs (English) |
| Author:
|
Zhang, Fuji |
| Author:
|
Chen, Zhibo |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
895-902 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\mathcal {D}$ of digraphs (graphs) is a limit point of eigenvalues of a set $\ddot{\mathcal {D}}$ of bipartite digraphs (graphs), where $\ddot{\mathcal {D}}$ consists of the double covers of the members in $\mathcal {D}$. 4. Every limit point of eigenvalues of a set $\mathcal {D}$ of digraphs is a limit point of eigenvalues of line digraphs of the digraphs in $\mathcal {D}$. 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. (English) |
| Keyword:
|
limit point |
| Keyword:
|
eigenvalue of digraph (graph) |
| Keyword:
|
double cover |
| Keyword:
|
subdivision digraph |
| Keyword:
|
line digraph |
| MSC:
|
05C50 |
| MSC:
|
15A48 |
| idZBL:
|
Zbl 1164.05412 |
| idMR:
|
MR2261661 |
| . |
| Date available:
|
2009-09-24T11:39:13Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128114 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
