What question did this study set out to answer?

This research aims to generalize the Tutte polynomial for vertex-weighted graphs and explore its connections to group cohomology.

January 6, 2026Open Access

Tutte Polynomials for Vertex-Weighted Graphs and Group Cohomology

Puntos clave

This research aims to generalize the Tutte polynomial for vertex-weighted graphs and explore its connections to group cohomology.
Introduced a generalization of the Tutte polynomial considering vertex and edge weights.
Analyzed the coefficients based on contraction-deletion relations depending on vertex weights.
Established the relationship between the polynomial coefficients and symmetric 2-cocycle relations.
The generalized Tutte polynomial aligns with group cohomology concepts.
The polynomial serves as a resource for deriving 4-invariants of graphs.
Insights into the application of these invariants within knot theory were provided.

Resumen

In the focus of my talk is a generalization of the Tutte polynomial for vertex-weighted and edge-weighted graphs, for which the coefficients of the contraction-deletion relation depend non-trivially on the vertex weights. We demonstrate that the corresponding coefficient relation coincides with the symmetric 2-cocycle relation in the group cohomology. Finally, we demonstrate that our polynomial is a rich source for constructing 4-invariants of graphs, which are very important in the knot theory.

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