| Ordering Quasi-Tree Graphs on $n$ Vertices by Their Spectral Radii |
| Received:April 20, 2017 Revised:May 17, 2017 |
| Key Words:
quasi-tree graph spectral radius extremal graph
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11171290) and the Natural Science Foundation of Jiangsu Province (Grant No.BK20151295). |
| Author Name | Affiliation | | Ke LUO | Department of Mathematics, Qinghai Normal University, Qinghai 810008, P. R. China
School of Mathematics and Statistics, Yancheng Teachers University, Jiangsu 224002, P. R. China | | Zhen LIN | Department of Mathematics, Qinghai Normal University, Qinghai 810008, P. R. China
School of Mathematics and Statistics, Yancheng Teachers University, Jiangsu 224002, P. R. China | | Shuguang GUO | School of Mathematics and Statistics, Yancheng Teachers University, Jiangsu 224002, 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. Liu and Lu [Linear Algebra Appl. 428 (2008) 2708-2714] determined the maximal spectral radius together with the corresponding graph among all quasi-tree graphs on $n$ vertices. In this paper, we extend their result, and determine the second to the fifth largest spectral radii together with the corresponding graphs among all quasi-tree graphs on $n$ vertices. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2018.02.002 |
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