Dehn colorings and vertex-weight invariants for spatial graphs

In this talk, we consider Dehn colorings for spatial graphs, and give a family of spatial graph invariants which are called vertex-weight invariants. The invariants are used to give the complete classification for vertex conditions of Dehn colorings. We give some examples of spatial graphs that can be distinguished by a vertex-weight invariant, whereas distinguished by neither their constituent links nor the number of Dehn colorings with no vertex condition. This is a joint work with Natsumi Oyamaguchi.