The King of Sedom came to greet Avraham in a location which the Pasuk describes as both "Emek Shaveh" and "Emek ha'Melech." What is the significance of these two descriptions?
Rashi #1: "Emek Shaveh" means a valley devoid of trees and of obstacles. "Emek ha'Melech" means that it served as the playing-ground of the king, which measured thirty canes (of six Amos). 1
Rashi #2: "Emek ha'Melech" was the valley where all the nations in the world met and crowned Avraham as king and leader over them.
Targum Onkelus and Targum Yonasan.