The Yamada polynomial of spatial graphs obtained by edge replacements
The Yamada polynomial of spatial graphs obtained by edge replacements
复制标题
边替换得到的空间图的山田多项式
DOI：
10.1142/s021821651842004x
复制
发表时间：
2018
影响因子：
0.5
通讯作者：
Vesnin Andrei
中科院分区：
文献类型：
--
作者：
Li Miaowang;Lei Fengchun;Li Fengling;Vesnin Andrei
我们提出了计算空间图的山田多项式的公式，该空间图是通过用空间部分替换平面图（例如循环图、θ图和花束图）的边而获得的。作为推论，表明某些系列空间图的 Yamada 多项式的零点在复平面的某个区域是密集的，由不等式组描述。此外，还得到了图的山田多项式与边标记图的链式多项式之间的关系。
We present formulae for computing the Yamada polynomial of spatial graphs obtained by replacing edges of plane graphs, such as cycle-graphs, theta-graphs, and bouquet-graphs, by spatial parts. As a corollary, it is shown that zeros of Yamada polynomials of some series of spatial graphs are dense in a certain region in the complex plane, described by a system of inequalities. Also, the relation between Yamada polynomial of graphs and the chain polynomial of edge-labeled graphs is obtained.