Classification of book representations of K6
Classification of book representations of K6
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K6图书表征分类
DOI：
10.1142/s0218216517500754
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发表时间：
2017
影响因子：
0.5
通讯作者：
D. Rowland
中科院分区：
文献类型：
--
作者：
D. Rowland
图形的书本表示是在三维空间中嵌入图形的一种特殊方式，因此顶点位于圆上，边缘是不相交拓扑磁盘上的弦。我们描述了保留环境同位素的书籍表示的一组操作，并将这些操作应用于K6，即具有六个顶点的完整图。我们证明了K6有59种不同的书本表示法，并确定了每种表示法中打结和链接循环的数量和类型。我们证明了K6的书本表示包含1到7个链接，以及多达9个结环。此外，在K6的书本表示中，所有的环和环的交叉数最多为4。
A book representation of a graph is a particular way of embedding a graph in three-dimensional space so that the vertices lie on a circle and the edges are chords on disjoint topological disks. We describe a set of operations on book representations that preserves ambient isotopy, and apply these operations to K6, the complete graph with six vertices. We prove there are exactly 59 distinct book representations for K6, and we identify the number and type of knotted and linked cycles in each representation. We show that book representations of K6 contain between one and seven links, and up to nine knotted cycles. Furthermore, all links and cycles in a book representation of K6 have crossing number at most four.