Ordering Quasi-tree Graphs on n Vertices by Their Spectral Radii
Received:April 29, 2017  Revised:May 09, 2017
Key Word: Quasi-tree graph   Spectral radius   Extremal graph
Fund ProjectL:The National Natural Science Foundation of China (Nos. 11171290) and the Natural Science Foundation of Jiangsu Province (BK20151295)
 Author Name Affiliation E-mail Shu-Guang Guo Yancheng Teachers University ychgsg@163.com Ke Luo Qinghai Normal University luoke_hn@163.com Zhen Lin Qinghai Normal University LNLinZhen@163.com
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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.