On the Laplacian energy of a graph

Mirjana Lazić

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 4, page 1207-1213
  • ISSN: 0011-4642

Abstract

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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 $\alpha =40$.

How to cite

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Lazić, Mirjana. "On the Laplacian energy of a graph." Czechoslovak Mathematical Journal 56.4 (2006): 1207-1213. <http://eudml.org/doc/31100>.

@article{Lazić2006,
abstract = {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 $\alpha =40$.},
author = {Lazić, Mirjana},
journal = {Czechoslovak Mathematical Journal},
keywords = {simple graphs; Laplacian spectrum; energy of a graph},
language = {eng},
number = {4},
pages = {1207-1213},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the Laplacian energy of a graph},
url = {http://eudml.org/doc/31100},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Lazić, Mirjana
TI - On the Laplacian energy of a graph
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 4
SP - 1207
EP - 1213
AB - 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 $\alpha =40$.
LA - eng
KW - simple graphs; Laplacian spectrum; energy of a graph
UR - http://eudml.org/doc/31100
ER -

References

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  1. Spectra of Graphs—Theory and Application, VEB Deutscher Verlag der Wissenschaften, Berlin-New York, 1980. (1980) MR0572262
  2. Recent Results in the Theory of Graph Spectra. Ann. Discrete Math.  36, North-Holland, Amsterdam, 1988. (1988) MR0926481
  3. 10.1016/0012-365X(84)90033-5, Discrete Math. 50 (1984), 37–49. (1984) MR0747710DOI10.1016/0012-365X(84)90033-5
  4. 10.1137/0611016, SIAM J.  Matrix Anal. Appl. 11 (1990), 218–238. (1990) MR1041245DOI10.1137/0611016
  5. Laplacian matrices of graphs. A survey, Linear Algebra and its Appl. 197, 198 (1994), 143–176. (1994) Zbl0802.05053MR1275613
  6. Graphs whose energy does not exceed  3, Czechoslovak Math. J. 36 (1986), 167–171. (1986) MR0831303

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