Final answer:
King Azaz the Unabridged and The Mathemagician rule over Dictionopolis and Digitopolis respectively in 'The Phantom Tollbooth', representing domains of language and mathematics.
Step-by-step explanation:
In the book The Phantom Tollbooth, the rulers over Dictionopolis are King Azaz the Unabridged and The Mathemagician, his brother, who rules over Digitopolis. Their respective domains are over words and numbers, embodying the realms of language and mathematics. Their rule is a central theme to the narrative, which showcases the mastery of language, imagination, and numbers as means to solve problems and navigate the world created by author Norton Juster.