There are many vegies that can be fed to dogs. Except Onions, Tomatoes not recommended but some do feed them. I would Not!
Do your research easily by searching in Google "foods to avoid feeding your dog" or "Foods Toxic to dogs".
NOTE: Too many vegetables, over time can possibly cause mineral deficiencies.
My dog eats low glycemic vegetables since she has some yeast issues. Vegetables that I don't feed her currently are carrots, peas, any potatoes including sweets and yams.
She does eat cucumbers, baby zucchini, cauliflower, asparagus, turnip, Brussel sprouts, beets (very little due to glycemic index) romaine lettuce centers, bok choy and has eaten broccoli, celery and I know I am forgetting a few.
I noticed red dots on my dogs privates so have since cut out high oxalate vegetables to avoid oxalate crystals.
Apparently, according to dogaware.com, dogs do not benefit nutritionally from carbohydrates although they do provide for antioxidants, trace minerals and most importantly, fiber.
In order for the dog to easily digest the vegetables, it is suggested to boil them lightly until cooked, drain and rinse well before mashing or pureeing.
Raw vegetables should be minced, to help aid in digestion.
Dogaware.com suggests that raw vegetables are not harmful but do not provide any nutritional benefit.
This makes sense to me as dogs diet is based on protein and fats.
This is a useful article that I will refer you too as it talks about fruit.
DogAware.com: Homemade Diets for Dogs
(scroll down to
"Guidelines for Raw Diets that Include Bones").
I can not comment on feeding fruit as my dog does not like to eat fruit, unfortunately, even though I do sneak bananas and apples into her meal at times.
Further interesting read concerning carbs:
FAT, CARBOHYDRATES AND FATTY ACIDS IN YOUR DOGS DIET