Lexical Definition

‎βασίλειος‎ basíleios (bas-il'-i-os) kingly ^G:A
from ‎βασιλεύς‎

royal.

• kingly (in nature)

Abbott-Smith

βασίλειος, -ον (also -α, -ον; < βασιλεύς), [in LXX; Ex 19:6, De 3:10 (מַמְלָכָה), Ex 23:22, Wi 18:15, III Mac 3:28, IV Mac 3:8*;]
royal: I Pe 2:9(LXX) (v. Hort, in l.).†

Abbott-Smith References

Liddell-Scott-Jones

βασίλειος-ειος, ον,

also α, ον [Refs 4th c.BC+]; Ionic dialect and Aeolic dialect βᾰσιλ-ήϊος, η, ον, also βᾰσιλ-ῇος Melinnoap.[Refs 5th c.AD+]:— royal, δεινὸν δὲ γένος βασιλήϊόν ἐστι κτείνειν [Refs 8th c.BC+]; used by Trag. in Lyric poetry, β. οἶκοι, μέλαθρα, [Refs 4th c.BC+]; ἰσχύς, τιάρα, [Refs]; νόστος ὁ β. the king's return,[Refs 5th c.BC+]; compare πῆχυς.

__2 of the archon βασιλεύς, ἡ β. στοά [Refs 4th c.BC+] (also of the basilica of Herod at Jerusalem, [Refs 1st c.AD+]
__3 'royal', i.e.choice, μύρον [Refs 7th c.BC+]; compare βασίλεια· γένος ἰσχάδων, [Refs 5th c.AD+]
__4 Ἄρτεμις βασιληΐη, divinity in Thrace, [Refs 5th c.BC+]