Which cities in arabia became part of the islamic empire during the time of muhammad?

By the time Muhammad there was no Islamic Empire. There were Emirates, Caliphates, and kingdoms. All Muslim, but no cohesive unity until the Caliphs of Baghdad took power. And then after the 1200s when the Mongols evaded and destroyed the cities of Iraq, the fractious relation of the Middle east took over and led them to division.

Where is the map ? u can attach it when asking a question btw