Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
simple graphs; Laplacian spectrum; energy of a graph
simple graphs; Laplacian spectrum; energy of a graph
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 $\alpha =40$.
References:
[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
[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
[3] D. Cvetković, M. Petrić: A table of connected graphs with six vertices. Discrete Math. 50 (1984), 37–49. DOI 10.1016/0012-365X(84)90033-5 | MR 0747710
[4] R. Grone, R. Merris, V. Sunder: The Laplacian spectrum of a graph. SIAM J. Matrix Anal. Appl. 11 (1990), 218–238. DOI 10.1137/0611016 | MR 1041245
[5] R. Merris: Laplacian matrices of graphs. A survey. Linear Algebra and its Appl. 197, 198 (1994), 143–176. MR 1275613 | Zbl 0802.05053
[6] A. Torgašev: Graphs whose energy does not exceed 3. Czechoslovak Math. J. 36 (1986), 167–171. MR 0831303
Search
Partner of
