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arXiv · 1712.00208

The full chracterazation of the graphs with a L-eigenvalue of multiplicity $n-3$

Daijun Yin·Qiongxiang Huang
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Abstract

Let $\mathcal{G}(n,k)$ be the set of connected graphs of order $n$ with one of the Laplacian eigenvalue having multiplicity $k$. It is well known that $\mathcal{G}(n,n-1)=\{K_n\}$. The graphs of $\mathcal{G}(n,n-2)$ are determined by Das, and the graphs of $\mathcal{G}(n,n-3)$ with four distinct Laplacian eigenvalues are determined by Mohammadian et al. In this paper, we determine the graphs of $\mathcal{G}(n,n-3)$ with three distinct Laplacian eigenvalues, and then the full characterization of the graphs in $\mathcal{G}(n,n-3)$ is completed.

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Daijun Yin, Qiongxiang Huang. 2017-12-01. The full chracterazation of the graphs with a L-eigenvalue of multiplicity $n-3$. https://arxiv.org/abs/1712.00208

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