| Title:
|
Remarks on spectral radius and Laplacian eigenvalues of a graph (English) |
| Author:
|
Zhou, Bo |
| Author:
|
Cho, Han Hyuk |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
781-790 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a graph with $n$ vertices, $m$ edges and a vertex degree sequence $(d_1, d_2, \dots , d_n)$, where $d_1 \ge d_2 \ge \dots \ge d_n$. The spectral radius and the largest Laplacian eigenvalue are denoted by $\rho (G)$ and $\mu (G)$, respectively. We determine the graphs with \[ \rho (G) = \frac{d_n - 1}{2} + \sqrt{2m - nd_n + \frac{(d_n +1)^2}{4}} \] and the graphs with $d_n\ge 1$ and \[ \mu (G) = d_n + \frac{1}{2} + \sqrt {\sum _{i=1}^n d_i (d_i-d_n) + \Bigl (d_n - \frac{1}{2} \Bigr )^2}. \] We also present some sharp lower bounds for the Laplacian eigenvalues of a connected graph. (English) |
| Keyword:
|
spectral radius |
| Keyword:
|
Laplacian eigenvalue |
| Keyword:
|
strongly regular graph |
| MSC:
|
05C07 |
| MSC:
|
05C50 |
| MSC:
|
05C75 |
| idZBL:
|
Zbl 1081.05068 |
| idMR:
|
MR2153101 |
| . |
| Date available:
|
2009-09-24T11:27:36Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128021 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
