Abstract
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.
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