december 2021 Extremal results on distance Laplacian spectral radius of graphs
Hongying Lin, Bo Zhou
Bull. Belg. Math. Soc. Simon Stevin 28(2): 233-254 (december 2021). DOI: 10.36045/j.bbms.190405

Abstract

The distance Laplacian spectral radius of a connected graph $G$ is the largest eigenvalue of its distance Laplacian matrix $\mathcal{L}(G)$ defined as $\mathcal{L}(G)=Tr(G)-D(G)$, where $Tr(G)$ is the diagonal matrix of vertex transmissions and $D(G)$ is the distance matrix of $G$. We determine the unique trees with maximum distance Laplacian spectral radius among trees of perfect matching with given maximum degree, the unique trees with second (third, respectively) maximum distance Laplacian spectral radius, and the unique bipartite unicyclic graphs with maximum distance Laplacian spectral radius. We also determine the unique graphs with minimum distance Laplacian spectral radius among bicyclic graphs.

Citation

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Hongying Lin. Bo Zhou. "Extremal results on distance Laplacian spectral radius of graphs." Bull. Belg. Math. Soc. Simon Stevin 28 (2) 233 - 254, december 2021. https://doi.org/10.36045/j.bbms.190405

Information

Published: december 2021
First available in Project Euclid: 23 December 2021

Digital Object Identifier: 10.36045/j.bbms.190405

Subjects:
Primary: 05C12 , 05C50 , 15A18‎

Keywords: bicyclic graphs , distance Laplacian spectral radius , distance matrix , extremal problem , trees , unicyclic graphs

Rights: Copyright © 2021 The Belgian Mathematical Society

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Vol.28 • No. 2 • december 2021
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