The generalized windmill graphs are good models for many real-world networks. In this paper, we obtain analytic expressions for the eigenvalues of the adjacency matrices and of the Laplacian matrices of the generalized windmill graphs. Using this information, we study some structural and dynamical properties of these graphs. To the end, we investigate the metro networks of four France cities and propose our suggestions for the planning of public transport networks.

中文翻译：

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广义风车网络的光谱：分析解决方案和应用

广义风车图是许多现实世界网络的好模型。在本文中，我们得到了广义风车图的邻接矩阵和拉普拉斯矩阵的特征值的解析表达式。利用这些信息，我们研究了这些图的一些结构和动力学特性。最后，我们调查了法国四个城市的地铁网络，并提出了我们对公共交通网络规划的建议。