Characterization of Graphs with Some Normalized Laplacian Eigenvalue Having Multiplicity $n{-}4$

Shaowei Sun

doi:10.1007/s40304-024-00395-5

Communications in Mathematics and Statistics ›› : 1 -11. DOI: 10.1007/s40304-024-00395-5

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Characterization of Graphs with Some Normalized Laplacian Eigenvalue Having Multiplicity $n{-}4$

Shaowei Sun ¹^,²^,^a

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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 $n\ge 25$ with some normalized Laplacian eigenvalue $\rho \in \big (0,\,\frac{n-1}{n-2}\big )$ having multiplicity $n{-4}$.

Keywords

Graph / Normalized Laplacian matrix / Multiplicity of eigenvalues

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Shaowei Sun. Characterization of Graphs with Some Normalized Laplacian Eigenvalue Having Multiplicity $n{-}4$. Communications in Mathematics and Statistics 1-11 DOI:10.1007/s40304-024-00395-5