# Loop-correction for non-commutative quartic theory

What is the meaning of the second, third and fourth graph? The image is from arXiv:hep-th/9912072.

2. Interestingly, non-planar graphs are suppressed due to extra phase factors. (This is somewhat similar to the planar limit/large-$$N_c$$-expansion in $$SU(N_c)$$ Yang-Mills theory, although the non-planar suppression is there caused because non-planar diagrams have fewer traces.)