| Maxima of the $Q$-Index for Halin Graphs |
| Received:May 20, 2016 Revised:March 15, 2017 |
| Key Words:
Halin graph signless Laplacian spectral radius wheel graph
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| Fund Project: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 Name | Affiliation | | 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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