A complex unit gain graph ( T -gain graph) Φ = G , φ ) is a where the function assigns number to each orientation of an edge and its inverse assigned opposite orientation. balanced if product gains oriented cycle (if any) 1. We propose two notions distance matrices D < max min Φ, for any ordering ‘<’ vertex set. characterize graphs which are independent ordering. show holds standard vertices on...

Graham and Winkler derived a formula for the determinant of distance matrix full-dimensional set n + 1 points { x 0 , … } in Hamming cube H = ( ? ) . In this article we derive D an arbitrary m It follows from more general that det ? if only vectors are affinely independent. Specializing to case provides new insights into original Winkler. A significant difference arises between cases < is noted...