Abstract

We construct a generalization of the Tutte polynomial for vertex-weighted graphs for which the coefficients of the “deletion–contraction” relation depend nontrivially on the vertex weights. We show that the corresponding relation on the coefficients coincides with the two-cocycle relation in the group cohomology. We obtain a representation of a new invariant by summing over subgraphs and establish its connection with four-invariants of graphs.

中文翻译：

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顶点加权图和群上同调的 Tutte 多项式

摘要

我们为顶点加权图构建了 Tutte 多项式的推广，其中“删除 - 收缩”关系的系数非常依赖于顶点权重。我们证明了系数的对应关系与群上同调中的二环关系一致。我们通过对子图求和来获得新不变量的表示，并建立其与图的四个不变量的连接。