具有五个不同于0和1的Laplacian特征值的单圈图

Unicyclic Graphs with Five Laplacian Eigenvalues Different from 0 and 1

中文关键词:  单圈图  拉普拉斯特征值  重数

英文关键词:unicyclic graph  Laplacian eigenvalue  multiplicity

中文摘要:

      设$U$是$n$阶单圈图, $m_{U}(1)$是$U$的拉普拉斯特征值1的重数.众所周知,0是连通图重数为1的拉普拉斯特征值.这意味着如果$U$有五个不同于0和1的拉普拉斯特征值,那么$m_U(1)=n-6$.本文完整刻画了$m_U(1)=n-6$的所有单圈图.

英文摘要:

      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 $m_{U}(1)=n-6$.