| Title:
|
Note on a conjecture for the sum of signless Laplacian eigenvalues (English) |
| Author:
|
Chen, Xiaodan |
| Author:
|
Hao, Guoliang |
| Author:
|
Jin, Dequan |
| Author:
|
Li, Jingjian |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
68 |
| Issue:
|
3 |
| Year:
|
2018 |
| Pages:
|
601-610 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a simple graph $G$ on $n$ vertices and an integer $k$ with $1\leq k\leq n$, denote by $\mathcal {S}_k^+(G)$ the sum of $k$ largest signless Laplacian eigenvalues of $G$. It was conjectured that $\mathcal {S}_k^+(G)\leq e(G)+{k+1 \choose 2}$, where $e(G)$ is the number of edges of $G$. This conjecture has been proved to be true for all graphs when $k\in \{1,2,n-1,n\}$, and for trees, unicyclic graphs, bicyclic graphs and regular graphs (for all $k$). In this note, this conjecture is proved to be true for all graphs when $k=n-2$, and for some new classes of graphs. (English) |
| Keyword:
|
sum of signless Laplacian eigenvalues |
| Keyword:
|
upper bound |
| Keyword:
|
clique number |
| Keyword:
|
girth |
| MSC:
|
05C50 |
| MSC:
|
15A18 |
| idZBL:
|
Zbl 06986959 |
| idMR:
|
MR3851878 |
| DOI:
|
10.21136/CMJ.2018.0548-16 |
| . |
| Date available:
|
2018-08-09T13:08:55Z |
| Last updated:
|
2020-10-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147355 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
