1 Kings 12:17

But as for the children of Israel which dwelt in the cities
of Judah
Either such Israelites of the ten tribes that had before dwelt, or now upon this removed, for the sake of worship, to dwell in the tribe of Judah; or else that part of Israel, the tribe of Judah, which dwelt in the cities belonging to it:

Rehoboam reigned over them;
they owned him to be their king, and submitted to his government.