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

• 作 者: Zhen LIN Shuguang GUO Lianying MIAO
• 机 构: School of Mathematics, China University of Mining and Technology, Jiangsu 221116, P.R.China;School o
• 出 处: 数学研究及应用
• 发表日期: 2020年5期
• 关键词: quasi-tree graph signless Laplacian matrix second largest eigenvalue sum of eige

A connected graph G =(V,E) is called a quasi-tree graph if there exists a vertex vo ∈ V(G) such that G-vo 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-5/4.