Abstract Explicit formulas for coordination sequences of all 20 plane 2-uniform graphs are proved. The proof is based on the concept of layer-by-layer growth and on the canonical representation of geodesic chains in terms of special chains called as rays. The method works for a wide class of plane periodic graphs satisfying the following condition: for each sector of layer-by-layer growth there exists a graph vertex that is initial for two rays determining the sector. This generaizes the previous results where it is required that all vertices are initial for all rays.

中文翻译：

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2-一致图的坐标序列

摘要 证明了所有20个平面2-均匀图的配位序列的显式公式。证明是基于逐层增长的概念和测地线链在称为射线的特殊链方面的规范表示。该方法适用于满足以下条件的多种平面周期图：对于逐层增长的每个扇区，存在一个图顶点，该顶点对于确定该扇区的两条射线是初始的。这产生了先前的结果，其中要求所有顶点对于所有光线都是初始的。