Unicyclic Graphs with Five Lapalcian Eigenvalues Different from 0 and 1
Received:September 04, 2020  Revised:January 03, 2021
Key Word: unicyclic graph   Laplacian eigenvalue   multiplicity  
Fund ProjectL: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).
Author NameAffiliation
Mengyue YUAN Institute of Applied Mathematics, Lanzhou Jiaotong University, Gansu 730070, P. R. China 
Fei WEN Institute of Applied Mathematics, Lanzhou Jiaotong University, Gansu 730070, P. R. China 
Muchun LI Institute of Applied Mathematics, Lanzhou Jiaotong University, Gansu 730070, P. R. China 
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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 Lapalcian 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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