On the second Laplacian spectral moment of a graph

Ying Liu; Yu Qin Sun

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 2, page 401-410
  • ISSN: 0011-4642

Abstract

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Kragujevac (M. L. Kragujevac: On the Laplacian energy of a graph, Czech. Math. J. 56(131) (2006), 1207–1213) gave the definition of Laplacian energy of a graph G and proved L E ( G ) ≥ 6 n - 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.

How to cite

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Liu, Ying, and Sun, Yu Qin. "On the second Laplacian spectral moment of a graph." Czechoslovak Mathematical Journal 60.2 (2010): 401-410. <http://eudml.org/doc/38015>.

@article{Liu2010,
abstract = {Kragujevac (M. L. Kragujevac: On the Laplacian energy of a graph, Czech. Math. J. 56(131) (2006), 1207–1213) gave the definition of Laplacian energy of a graph $G$ and proved $LE(G)\ge 6n-8$; 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.},
author = {Liu, Ying, Sun, Yu Qin},
journal = {Czechoslovak Mathematical Journal},
keywords = {Laplacian eigenvalues; Laplacian energy; chromatic number; complement; Laplacian eigenvalue; Laplacian energy; chromatic number; complement},
language = {eng},
number = {2},
pages = {401-410},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the second Laplacian spectral moment of a graph},
url = {http://eudml.org/doc/38015},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Liu, Ying
AU - Sun, Yu Qin
TI - On the second Laplacian spectral moment of a graph
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 2
SP - 401
EP - 410
AB - Kragujevac (M. L. Kragujevac: On the Laplacian energy of a graph, Czech. Math. J. 56(131) (2006), 1207–1213) gave the definition of Laplacian energy of a graph $G$ and proved $LE(G)\ge 6n-8$; 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.
LA - eng
KW - Laplacian eigenvalues; Laplacian energy; chromatic number; complement; Laplacian eigenvalue; Laplacian energy; chromatic number; complement
UR - http://eudml.org/doc/38015
ER -

References

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  1. Bondy, J. A., Murty, U. S. R., Graph Theory with Applications, North-Holland New York (1976). (1976) MR0411988
  2. Brooks, R. L., On coloring the nodes of a network, Proc. Cambridge Philos. Soc. 37 (1941), 194-197. (1941) MR0012236
  3. Brualdi, R. A., Goldwasser, J. L., 10.1016/0012-365X(84)90127-4, Discrete Math. 48 (1984), 1-21. (1984) Zbl0533.05043MR0732197DOI10.1016/0012-365X(84)90127-4
  4. Gutman, I., 10.1007/BF00552542, Theoret. Chim. Acta 45 (1977), 79-87. (1977) DOI10.1007/BF00552542
  5. Gutman, I., The energy of a graph, Ber. Math.-Stat. Sekt. Forschungszent. Graz 103 (1978), 1-22. (1978) Zbl0402.05040MR0525890
  6. Gutman, I., Acyclic conjugated molecules, trees and their energies, J. Math. Chem. 1 (1987), 123-143. (1987) MR0895532
  7. Lazi&apos;c, M. L., 10.1007/s10587-006-0089-2, Czechoslovak Math. J. 56 (2006), 1207-1213. (2006) Zbl1172.80301MR2280804DOI10.1007/s10587-006-0089-2

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