A degree preserving delta wye transformation with applications to 6-regular graphs and Feynman periods

We investigate a degree preserving variant of the $\Delta$-Y transformation which replaces triangle with new 6-valent vertex has double edges to vertices that had been in triangle. This operation is relevant for understanding scalar Feynman integrals 6 dimensions. study structure equivalence classes under this and its inverse, particular attention when are finite, they contain simple 6-regular graphs, doubled 3-regular graphs. The last these, particular, integral calculations, we make some observations linking these periods. Furthermore, properties minimal graphs classes.