Characterization of Graphs with Some Normalized Laplacian Eigenvalue Having Multiplicity

n-4

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Abstract

The spectrum of the normalized Laplacian matrix of a graph provides a lot of structural information of the graph, and it has applications in numerous areas and in different guises. In this paper, we completely characterize all connected graphs of order

n\ge 25

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with some normalized Laplacian eigenvalue

\rho \in (0,\frac{n-1}{n-2})

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\rho \in \big (0,\,\frac{n-1}{n-2}\big )$$\end{document}

having multiplicity

n-4

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.

Keywords

Graph / Normalized Laplacian matrix / Multiplicity of eigenvalues / 05C50 / 15A18

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Funding

National Natural Science Foundation of China(11901525)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature