Find Contacts with no Relationships
One way of achieving your goal would be via a temporary group:


Using advanced search, search for all contacts who do have a relationship (simply open the "Relationships" tab, enter nothing, and search - it will default to all active relationships).
Add all the resulting contacts to a group (or make a smart group if you want to save yourself this step in the future).
Using search-builder, find all contacts not in that group.


PS: the "Parent" contact sub-type has nothing to do with relationships. Contact types are quite different in CiviCRM from relationships, and having one does not automatically bestow the other.