Is there any specific law about vicarious liability of parents for child's negligent acts? What is the name of applicable laws?
Vicarious liability only applies to a master-servant or employer-employee relationship. This principle cannot be used in such a case.
A child can be found liable under negligence.
The standard of care is of a reasonable child of the same age. And the child has to be old enough to understand that their actions are unreasonable
The child can be sued, but not the parents. In some cases the court will order a child to pay after they've grown up.