| Title:
|
On eigenvectors of mixed graphs with exactly one nonsingular cycle (English) |
| Author:
|
Fan, Yi-Zheng |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
1215-1222 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a mixed graph. The eigenvalues and eigenvectors of $G$ are respectively defined to be those of its Laplacian matrix. If $G$ is a simple graph, [M. Fiedler: A property of eigenvectors of nonnegative symmetric matrices and its applications to graph theory, Czechoslovak Math. J. 25 (1975), 619–633] gave a remarkable result on the structure of the eigenvectors of $G$ corresponding to its second smallest eigenvalue (also called the algebraic connectivity of $G$). For $G$ being a general mixed graph with exactly one nonsingular cycle, using Fiedler’s result, we obtain a similar result on the structure of the eigenvectors of $G$ corresponding to its smallest eigenvalue. (English) |
| Keyword:
|
mixed graphs |
| Keyword:
|
Laplacian eigenvectors |
| MSC:
|
05C50 |
| MSC:
|
15A18 |
| idZBL:
|
Zbl 1174.05075 |
| idMR:
|
MR2357587 |
| . |
| Date available:
|
2009-09-24T11:52:28Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128234 |
| . |
| Reference:
|
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