
A green discharge can be a result of early uterine placental detachment - but after only a week into the pregnancy would suggest this isn't what you are seeing. At this point, however there may well be some (normal season) discharge because she'll still be in season - for the full 21 days, whether bred or not. I'd get her look at by your vet - sometimes a bitch can pick up an infection when being mated.
One of mine went back into a blood coloured minor discharge for the final week of her season after being mated - I was concerned because I'd not seen this happen before in my bitches, mated or not. However she had an uneventful pregnancy and 9 super, healthy puppies. So good that we kept 3 and brought them back from Canada to the UK where 2 were very successful in the ring here - and their brother, used just twice outside our kennel, and once by me, is back of a lot of successful UK Bassets now.