They all (birds, dogs and alligators) share a common ancestor. They share many characteristics, for example, they all have two eyes and their limbs are homologous in structure. Homology is the presence of common characteristics (in the simplest terms). Dogs, birds and alligators share a common tetrapod (species with four limbs) as an ancestor. Dogs and alligators still have those four limbs and use them for motion; whereas birds, while retaining two limbs, have evolved the forelimbs as wings. Another commonality from the tetrapod ancestor is the presence of five digits on the limbs. Dogs and alligators still have them, whereas in the case of birds, evolution has led to fusing of some of these digits together. So there exists homology between the three species mentioned in the question, just remember that evolution has led to some heterology.
They all have vertebrates
In addition to the above answer, birds, dogs, alligators - three of them are classified under same phylum chordata and same sub phylum vertebrata...which have the following same characters -
1. They have notochord present at some or all stages of life.
2. They have a dorsal nerve chord.
3. They are bilaterally symmetrical, coelomate and triploblastic.
4. They have paired gill pouches.