I studied animal nutrition as part of a course as college I did, and as part of a project we were required to write a detailed report comparing two animal diets and their digestive systems (I chose dogs and cows). :) I'm not a vet though, so always make sure to research everything yourself.
Dogs can indeed live on a vegan diet, as they can produce the proteins they need. However, it's not the best option for them. Good quality food with no grain is the best way to go, either by feeding high-quality dog food such as Orijen, or feeding a raw diet. Diets like the Prey Model are my personal favourite, though anyone wanting to try this PLEASE do the research as to make sure your dog's getting a good balance of food. It's basically whole carcasses, fresh bones with a lot of muscle meat, and the right balance of a mix of organs. Some grated veggies and whole eggs are good too. It's high-energy so your dog eats less, has more energy but is calmer, and doesn't smell doggy all the time!
I'm not keen on feeding dogs a vegan diet because it seems a bit wrong to me to deprive an animal of what it's 'supposed' to eat and forcing a completely different diet on it. Some dogs will happily eat a vegan diet, sure, but some dogs will also happily eat poop and tennis balls.