The mayor and council of each city shall have authority: to regulate the running at large of domesticated animals; to cause such as may be running at large to be impounded and sold to discharge the penalties and costs of impounding, keeping and sale; to impose a license tax upon the owners and harborers and enforce the same by appropriate penalties; to authorize the destruction or sale of any domesticated animal, the owner or harborer of which shall neglect or refuse to pay such license tax; to provide for the erection of all needful pens and pounds within or without the city limits; and to appoint and compensate keepers thereof, and to establish and enforce rules governing the same.