拟树图按第二大无符号拉普拉斯特征值排序

Ordering Quasi-Tree Graphs by the Second Largest Signless Laplacian Eigenvalues

中文关键词:  拟树图  无符号拉普拉斯矩阵  第二大特征值  特征值的和  排序

英文关键词:quasi-tree graph  signless Laplacian matrix  second largest eigenvalue  sum of eigenvalues  ordering

中文摘要:

      若连通图$G=(V, E)$中存在点$v_0\inV(G)$,使得$G-v_0$是树,则称$G$是拟树图.在本文中,我们确定了第二大无符号拉普拉斯特征值大于等于$n-3$的所有$n$阶拟树图.作为应用,我们给出了前两个最大无符号拉普拉斯特征值之和大于$2n-\frac{5}{4}$的所有$n$阶拟树图.

英文摘要:

      A connected graph $G=(V, E)$ is called a quasi-tree graph if there exists a vertex $v_0\in V(G)$ such that $G-v_0$ is a tree. In this paper, we determine all quasi-tree graphs of order $n$ with the second largest signless Laplacian eigenvalue greater than or equal to $n-3$. As an application, we determine all quasi-tree graphs of order $n$ with the sum of the two largest signless Laplacian eigenvalues greater than to $2n-\frac{5}{4}$.