Geodesic
New bounds on the Laplacian spectral ratio of connected graphs
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 4, pp. 1207-1220
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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).
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).
DOI : 10.21136/CMJ.2024.0170-24
Classification : 05C05, 05C50
Keywords: Laplacian eigenvalue; ratio; tree; bound 
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Lin, Zhen; Cai, Min; Wang, Jiajia. New bounds on the Laplacian spectral ratio of connected graphs. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 4, pp. 1207-1220. doi: 10.21136/CMJ.2024.0170-24

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