Tutte Polynomials for Vertex-Weighted Graphs and Group Cohomology

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.