| Ordering Quasi-Tree Graphs by the Second Largest Signless Laplacian Eigenvalues |
| Received:September 04, 2019 Revised:March 17, 2020 |
| Key Words:
quasi-tree graph signless Laplacian matrix second largest eigenvalue sum of eigenvalues ordering
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| Fund Project: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). |
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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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