| Title:
|
On Laplacian eigenvalues of connected graphs (English) |
| Author:
|
Milovanović, Igor Ž. |
| Author:
|
Milovanović, Emina I. |
| Author:
|
Glogić, Edin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
529-535 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be an undirected connected graph with $n$, $n\ge 3$, vertices and $m$ edges with Laplacian eigenvalues $\mu _1\ge \mu _2 \ge \cdots \ge \mu _{n-1}>\mu _n =0$. Denote by $\mu _I =\mu _{r_1}+\mu _{r_2} +\cdots +\mu _{r_k}$, $1\le k\le n-2$, $1\le r_1<r_2<\cdots <r_k\le n-1$, the sum of $k$ arbitrary Laplacian eigenvalues, with $\mu _{I_1}=\mu _1+\mu _2+\cdots +\mu _k$ and $\mu _{I_n}=\mu _{n-k}+\cdots +\mu _{n-1}$. Lower bounds of graph invariants $\mu _{I_1}-\mu _{I_n}$ and ${\mu _{I_1}}/{\mu _{I_n}}$ are obtained. Some known inequalities follow as a special case. (English) |
| Keyword:
|
Laplacian eigenvalues |
| Keyword:
|
linear spread |
| Keyword:
|
ratio spread |
| MSC:
|
05C50 |
| MSC:
|
15A18 |
| idZBL:
|
Zbl 06486962 |
| idMR:
|
MR3360442 |
| DOI:
|
10.1007/s10587-015-0191-4 |
| . |
| Date available:
|
2015-06-16T18:04:08Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144285 |
| . |
| Reference:
|
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| . |
