| Title:
|
On the second Laplacian spectral moment of a graph (English) |
| Author:
|
Liu, Ying |
| Author:
|
Sun, Yu Qin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
401-410 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Kragujevac (M. L. Kragujevac: On the Laplacian energy of a graph, Czech. Math. J. {\it 56}({\it 131}) (2006), 1207--1213) gave the definition of Laplacian energy of a graph $G$ and proved $LE(G)\geq 6n-8$; equality holds if and only if $G=P_n$. In this paper we consider the relation between the Laplacian energy and the chromatic number of a graph $G$ and give an upper bound for the Laplacian energy on a connected graph. (English) |
| Keyword:
|
Laplacian eigenvalues |
| Keyword:
|
Laplacian energy |
| Keyword:
|
chromatic number |
| Keyword:
|
complement |
| MSC:
|
05C50 |
| idZBL:
|
Zbl 1224.05312 |
| idMR:
|
MR2657957 |
| . |
| Date available:
|
2010-07-20T16:47:39Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140577 |
| . |
| Reference:
|
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| Reference:
|
[2] Brooks, R. L.: On coloring the nodes of a network.Proc. Cambridge Philos. Soc. 37 (1941), 194-197. MR 0012236 |
| Reference:
|
[3] Brualdi, R. A., Goldwasser, J. L.: Permanent of the Laplacian matrix of trees and bipartite graphs.Discrete Math. 48 (1984), 1-21. Zbl 0533.05043, MR 0732197, 10.1016/0012-365X(84)90127-4 |
| Reference:
|
[4] Gutman, I.: Acyclic systems with extremal Hückel $\pi$-electron energy.Theoret. Chim. Acta 45 (1977), 79-87. 10.1007/BF00552542 |
| Reference:
|
[5] Gutman, I.: The energy of a graph.Ber. Math.-Stat. Sekt. Forschungszent. Graz 103 (1978), 1-22. Zbl 0402.05040, MR 0525890 |
| Reference:
|
[6] Gutman, I.: Acyclic conjugated molecules, trees and their energies.J. Math. Chem. 1 (1987), 123-143. MR 0895532 |
| Reference:
|
[7] Lazi'c, M. L.: On the Laplacian energy of a graph.Czechoslovak Math. J. 56 (2006), 1207-1213. Zbl 1172.80301, MR 2280804, 10.1007/s10587-006-0089-2 |
| . |
