This is what I'm referring to. Just like Fresnel, at an angle, the green on the side gets darker. As seen in the glass slab in this image.
The edges like the rest of the glass have reflections that will have Fresnel effects visible on them. The edges are usually a lot rougher so the effects will be less visible, however the color and darkness of the glass does not depend on those Fresnel reflections directly. We see darker and more saturated color there because internal reflections and the roughness of the edge makes it possible to see the light that passes through a lot more glass and a lot more of the light is absorbed that way than what we see looking through the thinner side of the glass.
You can replicate that with simple glass shader and volume absorption:
I am using two identical materials in the example, except the one on the edges has a lot more roughness. Glass edges are usually sanded and are a lot rougher. You could achieve this with a roughness image texture as well.
Be aware that all the light that goes trough this glass is caustics, so it takes a really long time to render if you wish a realistic result. You could also fake this with transparent shader mixed with glossy by Fresnel for reflections and another color shader for the edges if it is not a very well visible object in your scene to avoid extremely long render times.