Neosporin® contains three antibiotics: bacitracin, neomycin, and polymyxin B. They together kill bacteria on the skin and prevent an infection in the wound.
Bacitracin is safe for dogs, as polymyxin B. However, neomycin apparently has been linked to loss of hearing with intravenous use in some cases, so it is recommended that you do not aplly neomycin to your dog without first consulting your vet.