| Title:
|
On the multiplicity of Laplacian eigenvalues for unicyclic graphs (English) |
| Author:
|
Wen, Fei |
| Author:
|
Huang, Qiongxiang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
72 |
| Issue:
|
2 |
| Year:
|
2022 |
| Pages:
|
371-390 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a connected graph of order $n$ and $U$ a unicyclic graph with the same order. We firstly give a sharp bound for $m_{G}(\mu )$, the multiplicity of a Laplacian eigenvalue $\mu $ of $G$. As a straightforward result, $m_{U}(1)\le n-2$. We then provide two graph operations (i.e., grafting and shifting) on graph $G$ for which the value of $m_{G}(1)$ is nondecreasing. As applications, we get the distribution of $m_{U}(1)$ for unicyclic graphs on $n$ vertices. Moreover, for the two largest possible values of $m_{U}(1)\in \{n-5,n-3\}$, the corresponding graphs $U$ are completely determined. (English) |
| Keyword:
|
unicyclic graph |
| Keyword:
|
Laplacian eigenvalue |
| Keyword:
|
multiplicity |
| Keyword:
|
bound |
| MSC:
|
05C50 |
| idZBL:
|
Zbl 07547210 |
| idMR:
|
MR4412765 |
| DOI:
|
10.21136/CMJ.2022.0499-20 |
| . |
| Date available:
|
2022-04-21T19:00:04Z |
| Last updated:
|
2024-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150407 |
| . |
| Reference:
|
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