| Unicyclic Graphs with Five Laplacian Eigenvalues Different from 0 and 1 |
| Received:September 04, 2020 Revised:January 03, 2021 |
| Key Words:
unicyclic graph Laplacian eigenvalue multiplicity
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11961041) and Excellent postgraduates of Gansu Provincial Department of Education ``Star of innovation'' Foundation (Grant No.2021CXZX-594). |
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| Abstract: |
| Let $U$ be a unicyclic graph of order $n$, and $m_{U}(1)$ the multiplicity of Laplacian eigenvalue $1$ of $U$. It is well-known that $0$ is a simple Laplacian eigenvalue of connected graph. This means that if $U$ has five Laplacian eigenvalues different from $0$ and $1$, then $m_{U}(1)=n-6$. In this paper, we completely characterize all the unicyclic graphs with $m_{U}(1)=n-6$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2021.06.002 |
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