Coordination sequences of 2-uniform graphs
Coordination sequences of 2-uniform graphs
复制标题
2-均匀图的协调序列
DOI：
10.1515/zkri-2020-0002
复制
发表时间：
2020
期刊：
影响因子：
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通讯作者：
A. Maleev
中科院分区：
文献类型：
--
作者：
A. Shutov;A. Maleev
摘要 证明了所有20个平面2-一致图的配位序列的显式公式。该证明基于逐层增长的概念以及测地链以称为射线的特殊链的规范表示。该方法适用于满足以下条件的一类广泛的平面周期图：对于逐层生长的每个扇区，存在一个图顶点，该顶点对于确定该扇区的两条射线来说是初始的。这生成了先前的结果，其中要求所有顶点对于所有光线都是初始的。
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.