| Title:
|
On the Laplacian energy of a graph (English) |
| Author:
|
Lazić, Mirjana |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
1207-1213 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider the energy of a simple graph with respect to its Laplacian eigenvalues, and prove some basic properties of this energy. In particular, we find the minimal value of this energy in the class of all connected graphs on $n$ vertices $(n=1,2,\ldots )$. Besides, we consider the class of all connected graphs whose Laplacian energy is uniformly bounded by a constant $\alpha \ge 4$, and completely describe this class in the case $\alpha =40$. (English) |
| Keyword:
|
simple graphs |
| Keyword:
|
Laplacian spectrum |
| Keyword:
|
energy of a graph |
| MSC:
|
05C50 |
| idZBL:
|
Zbl 1164.05408 |
| idMR:
|
MR2280804 |
| . |
| Date available:
|
2009-09-24T11:42:17Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128140 |
| . |
| Reference:
|
[1] D. Cvetković, M. Doob, and H. Sachs: Spectra of Graphs—Theory and Application.VEB Deutscher Verlag der Wissenschaften, Berlin-New York, 1980. MR 0572262 |
| Reference:
|
[2] D. Cvetković, M. Doob, I. Gutman, and A. Torgašev: Recent Results in the Theory of Graph Spectra. Ann. Discrete Math. 36.North-Holland, Amsterdam, 1988. MR 0926481 |
| Reference:
|
[3] D. Cvetković, M. Petrić: A table of connected graphs with six vertices.Discrete Math. 50 (1984), 37–49. MR 0747710, 10.1016/0012-365X(84)90033-5 |
| Reference:
|
[4] R. Grone, R. Merris, V. Sunder: The Laplacian spectrum of a graph.SIAM J. Matrix Anal. Appl. 11 (1990), 218–238. MR 1041245, 10.1137/0611016 |
| Reference:
|
[5] R. Merris: Laplacian matrices of graphs. A survey.Linear Algebra and its Appl. 197, 198 (1994), 143–176. Zbl 0802.05053, MR 1275613 |
| Reference:
|
[6] A. Torgašev: Graphs whose energy does not exceed 3.Czechoslovak Math. J. 36 (1986), 167–171. MR 0831303 |
| . |
