Calculating the fine structure constant in Feynman diagrams

[Phys12]

Griffith's Introduction to Elementary Particles, if I understand it correctly, states that in QED, the fine structure constant contributes less and less to the strength of the EM interaction as we add more and more vertices since the constant is so small (1/137). However, in QCD, since the constant is greater 1, it contributes more and more.

However, if you add 137 vertices, wouldn't that result in a constant of 1? And as you add more and more, you'll get higher values of the fine structure constant. Or do you multiply them so it gets smaller in QED, but larger in QCD.

 

[PeterDonis]

Or do you multiply them

If you are computing the amplitude for a Feynman diagram with multiple vertices, the constants for each vertex are multiplied.