Ordering Quasi-Tree Graphs on $n$ Vertices by Their Spectral Radii
Received:April 20, 2017  Revised:May 17, 2017
Key Word: quasi-tree graph   spectral radius   extremal graph  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11171290) and the Natural Science Foundation of Jiangsu Province (Grant No.BK20151295).
Author NameAffiliation
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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