Dedicated ip's have a history?

There was a domain I had from a month or so ago, that was sold, which had links in common with another site I’m n now introducing.

Never heard of this topic before - but what chances are there that G or anyone tracks subsequent domains by a dedicated address/per site owner?

There is nothing to worry about common links… As far as history is concerned, once the domain gets expired, everything associated with it gets wiped out