Feynman diagrams were introduced by physicists. They arise naturally
in mathematics (from knots and singular knots), and in molecular
biology (from RNA folding). In particular, work of G. Vernizzi, H.
Orland, and A. Zee
has shown that the genus of Feynman diagrams plays an important role
in the prediction of RNA structures.
The transition polynomial for 4-regular graphs was defined by Jaeger to
unify polynomials given by vertex reconfigurations similar to the