[n120cky]

I made this speculation on assumption Kuroyuki Hime family name is Yuuki.

Spoiler for Speculation on Black Lotus and Graphite Edge Family relation:

I think Kuroyuki hime is child of Asuna's brother so kuroyuki hime could have Yuuki family name, and Graphite Edge is KiritoxAsuna child that would make Black Lotus and Graphite Edge a cousin, that make sense that GE teach his/her cousin a move that will help her in Accel World.