特殊空间图的Yamada多项式计算
Calculation of Yamada Polynomials for Special Spatial Graphs
DOI: 10.12677/aam.2026.152074, PDF,    科研立项经费支持
作者: 邢琪睿*, 王欣瑞：辽宁师范大学数学学院，辽宁 大连
关键词: Yamada多项式；空间图；顶点数；交叉点数；The Yamada Polynomial； Spatial Graphs； Number of Vertices； Number of Crossings
摘要: Yamada多项式是刻画空间图拓扑特征的重要多项式不变量。本文以顶点数与交叉点数为分类维度研究特殊空间图的Yamada多项式，推导了一类特定单顶点螺旋图、2个顶点含0~3个交叉点的特殊空间图的Yamada多项式表达式，为复杂空间图的多项式计算提供了参考案例。
Abstract: The Yamada polynomial is a crucial polynomial invariant for characterizing the topological features of spatial graphs. Taking the number of vertices and crossings as the classification dimensions, this paper investigates the Yamada polynomials of special spatial graphs, deduces the expressions of the Yamada polynomials for special spatial graphs with one vertex and n crossings and those with two vertices and 0~3 crossings, and provides reference cases for the polynomial calculation of complex spatial graphs.
文章引用：邢琪睿, 王欣瑞. 特殊空间图的Yamada多项式计算[J]. 应用数学进展, 2026, 15(2): 337-344. https://doi.org/10.12677/aam.2026.152074

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