New bounds on the Laplacian spectral ratio of connected graphs

Zhen Lin; Min Cai; Jiajia Wang

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 4, page 1207-1220
  • ISSN: 0011-4642

Abstract

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Let G be a simple connected undirected graph. The Laplacian spectral ratio of G is defined as the quotient between the largest and second smallest Laplacian eigenvalues of G , which is an important parameter in graph theory and networks. We obtain some bounds of the Laplacian spectral ratio in terms of the number of the spanning trees and the sum of powers of the Laplacian eigenvalues. In addition, we study the extremal Laplacian spectral ratio among trees with n vertices, which improves some known results of Z. You and B. Liu (2012).

How to cite

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Lin, Zhen, Cai, Min, and Wang, Jiajia. "New bounds on the Laplacian spectral ratio of connected graphs." Czechoslovak Mathematical Journal 74.4 (2024): 1207-1220. <http://eudml.org/doc/299605>.

@article{Lin2024,
abstract = {Let $G$ be a simple connected undirected graph. The Laplacian spectral ratio of $G$ is defined as the quotient between the largest and second smallest Laplacian eigenvalues of $G$, which is an important parameter in graph theory and networks. We obtain some bounds of the Laplacian spectral ratio in terms of the number of the spanning trees and the sum of powers of the Laplacian eigenvalues. In addition, we study the extremal Laplacian spectral ratio among trees with $n$ vertices, which improves some known results of Z. You and B. Liu (2012).},
author = {Lin, Zhen, Cai, Min, Wang, Jiajia},
journal = {Czechoslovak Mathematical Journal},
keywords = {Laplacian eigenvalue; ratio; tree; bound},
language = {eng},
number = {4},
pages = {1207-1220},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {New bounds on the Laplacian spectral ratio of connected graphs},
url = {http://eudml.org/doc/299605},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Lin, Zhen
AU - Cai, Min
AU - Wang, Jiajia
TI - New bounds on the Laplacian spectral ratio of connected graphs
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 4
SP - 1207
EP - 1220
AB - Let $G$ be a simple connected undirected graph. The Laplacian spectral ratio of $G$ is defined as the quotient between the largest and second smallest Laplacian eigenvalues of $G$, which is an important parameter in graph theory and networks. We obtain some bounds of the Laplacian spectral ratio in terms of the number of the spanning trees and the sum of powers of the Laplacian eigenvalues. In addition, we study the extremal Laplacian spectral ratio among trees with $n$ vertices, which improves some known results of Z. You and B. Liu (2012).
LA - eng
KW - Laplacian eigenvalue; ratio; tree; bound
UR - http://eudml.org/doc/299605
ER -

References

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