Abstract We propose a new method to calculate topological densities of periodic graphs based on the concept of layer-by-layer growth. Topological density is expressed in terms of metric characteristics: the volume of the fundamental domain and the volume of the growth polytope of the graph. Our method is universal (works for all d-periodic graphs) and is easily automated. As examples, we calculate topological densities of all 20 plane 2-uniform graphs and 14 carbon allotrope modifications.

中文翻译：

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周期图的拓扑密度

摘要 基于逐层生长的概念，我们提出了一种计算周期图拓扑密度的新方法。拓扑密度用度量特征表示：图的基本域的体积和生长多胞体的体积。我们的方法是通用的（适用于所有 d-周期图）并且很容易实现自动化。例如，我们计算了所有 20 个平面 2-均匀图和 14 个碳同素异形体修饰的拓扑密度。