Maxima of the $Q$-Index for Halin Graphs
Received:May 20, 2016  Revised:March 15, 2017
Key Word: Halin graph   signless Laplacian spectral radius   wheel graph  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11171273) and the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University (Grant No.Z2016170).
Author NameAffiliation
Qi KONG Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Shaanxi 710072, P. R. China 
Ligong WANG Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Shaanxi 710072, P. R. China 
Yong LU Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Shaanxi 710072, P. R. China 
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Abstract:
      The $Q$-index of a graph $G$ is the largest eigenvalue $q(G)$ of its signless Laplacian matrix $Q(G)$. In this paper, we prove that the wheel graph $W_{n}=K_{1}\vee C_{n-1}$ is the unique graph with maximal $Q$-index among all Halin graphs of order $n$. Also we obtain the unique graph with second maximal $Q$-index among all Halin graphs of order $n$.
Citation:
DOI:10.3770/j.issn:2095-2651.2017.03.001
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