| Title:
|
Bounds for the (Laplacian) spectral radius of graphs with parameter $\alpha $ (English) |
| Author:
|
Tian, Gui-Xian |
| Author:
|
Huang, Ting-Zhu |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
567-580 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a simple connected graph of order $n$ with degree sequence $(d_1,d_2,\ldots ,d_n)$. Denote $(^\alpha t)_i = \sum \nolimits _{j\colon i \sim j} {d_j^\alpha }$, $(^\alpha m)_i = {(^\alpha t)_i }/{d_i^\alpha }$ and $(^\alpha N)_i = \sum \nolimits _{j\colon i \sim j} {(^\alpha t)_j }$, where $\alpha $ is a real number. Denote by $\lambda _1(G)$ and $\mu _1(G)$ the spectral radius of the adjacency matrix and the Laplacian matrix of $G$, respectively. In this paper, we present some upper and lower bounds of $\lambda _1(G)$ and $\mu _1(G)$ in terms of $(^\alpha t)_i $, $(^\alpha m)_i $ and $(^\alpha N)_i $. Furthermore, we also characterize some extreme graphs which attain these upper bounds. These results theoretically improve and generalize some known results. (English) |
| Keyword:
|
graph |
| Keyword:
|
adjacency matrix |
| Keyword:
|
Laplacian matrix |
| Keyword:
|
spectral radius |
| Keyword:
|
bound |
| MSC:
|
05C50 |
| MSC:
|
15A18 |
| idZBL:
|
Zbl 1265.05418 |
| idMR:
|
MR2990195 |
| DOI:
|
10.1007/s10587-012-0030-9 |
| . |
| Date available:
|
2012-06-08T09:54:18Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142847 |
| . |
| Reference:
|
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