While in the Indo-European traditions , gods were associated with Wolves often submitted to them and not dogs is quite understandable: Wolves represents the undomable instincts that needs to be submitted under an authority.
But in Hinduism it plays different roles. In Hindu mythology, the dog is the most inauspicious of animals, to be kept away from wedding ...
In one of the answers, it was mentioned as follows:
येषामीशे पशुपतिः पशूनां चतुष्पदामुत च द्विपदम् ।। [YajurVeda 3.1.4]
Which Pashus do the Pashupati rules? He rules both the two footed and four footed.
A forerunner for this concept is available in Rig Veda I.114.1 & 9, dedicated to Rudra, in a subtle manner.
इ॒मा रु॒द्राय॑ त॒वसे॑ ...