Halin图$Q$-谱半径的最大值

Maxima of the $Q$-Index for Halin Graphs

中文关键词:  Halin图  无符号拉普拉斯谱半径  轮图

英文关键词:Halin graph  signless Laplacian spectral radius  wheel graph

中文摘要:

      图$G$的$Q$-谱半径是图$G$对应的无符号拉普拉斯矩阵的最大特征值. 在这篇文章里, 我们证明了在具有$n$ 个顶点的Halin图中, 轮图 $W_{n}=K_{1}\vee C_{n-1}$是唯一的具有最大$Q$-谱半径的图. 同时, 我们也得到了在具有$n$个顶点的Halin图中, 具有第二大$Q$-谱半径的唯一图.

英文摘要:

      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 $n$.