Ordering Quasi-Tree Graphs by the Second Largest Signless Laplacian Eigenvalues
Received:September 04, 2019  Revised:March 17, 2020
Key Word: quasi-tree graph   signless Laplacian matrix   second largest eigenvalue   sum of eigenvalues   ordering  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11771443), the Fundamental Research Funds for the Central Universities (Grant No.2018BSCXB24) and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No.KYCX18_1980).
Author NameAffiliation
Zhen LIN School of Mathematics, China University of Mining and Technology, Jiangsu 221116, P. R. China 
Shuguang GUO School of Mathematics and Statistics, Yancheng Teachers University, Jiangsu 224002, P. R. China 
Lianying MIAO School of Mathematics, China University of Mining and Technology, Jiangsu 221116, P. R. China 
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Abstract:
      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 $2n-\frac{5}{4}$.
Citation:
DOI:10.3770/j.issn:2095-2651.2020.05.002
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