The context of the miracle of expulsion of demons from a man indicate both divine authority of Jesus, His Divinity or God-ness, and at the same time His difference from God-the-Father, for even the demons worship Him, ῾falling in front of Him῾ (προσέπεσεν; Mark has it "worshiped Him" - προσεκύνησεν /Mark5:6/) and call Him in the same episode the "Son of the Most High God" (Luke 8:28). Thus the demons both tremblingly and in awe give Him the same worship as befits to God, affirming in this way His equality, equal authority and sovereignty with His Father, and, at the same time, distinguish Him (the Son) from Him (the Father).
They, the demons, recognized the full divine authority in Him because He did not ask God in prayers that the demons may be expelled from the afflicted man, but even before demons started supplicating Him, with His sovereign authority Jesus commanded them (παρήγγειλεν) to go out from the man. Such an authority is not a province of even the highest of the angels, for the angels, first, are not worshiped by demons, and second, cannot command directly demons, but only by addressing to the name of Lord - "but even the archangel Michael, when he was disputing with the devil about the body of Moses, did not himself dare to condemn him for slander but said, “The Lord rebuke you!” /Jude 1:9/); however, Jesus as the Son of God is the one whom angels and demons - the first joyfully and the second tremblingly - worship alongside with God-the-Father.
In fact, Luke shows and tells implicitly what John tells plainly, that the Father's and the Son's divine activity is one and the same activity ("My Father acts to this day (i.e. always) and I act" (John 5:17) and “the Son can do nothing by himself: He can do only what He sees His Father doing, because whatever the Father does the Son also does" (John 5:19), and the same is true of he Father also: as He is totally impotent to create world without His ever-existing Logos, for everything is created through Him (John 1:3; Col. 1:16 etc.), so also He is totally impotent to expel demons from men and thus save them, but through Jesus - the incarnate Logos (just as Jesus is unable to do this without the Father).
Now, the full divine authority and sovereignty of Jesus was understood not only by the demons, but also by the demon-possessed man himself, who, after having been cleansed from the demonic possession was made wise by God so as to see, to weigh all things and make a conclusion that since Jesus expelled demons from him not through prayers, but through His own divine sovereignty, thus it was meet and correct from his side to acknowledge His Godhead. Therefore, when Jesus commanded him to tell all what God has done to him, he told everyone what Jesus has done to him, knowing that God-the-Father could in no way expel demons from him but only through His co-Sovereign Son.