Strong unique independence graph

Strong unique independence graph --- строго единственный граф независимости.

A graph [math]\displaystyle{ G }[/math] is a strong unique independence graph, if [math]\displaystyle{ G }[/math] is bipartite and has a unique [math]\displaystyle{ \beta(G) }[/math]-set. ([math]\displaystyle{ \beta(G) }[/math] is the independence number).

Theorem(G. Hopkins, W. Staton). A tree is a strong unique independence tree if and only if the distance between any pair of its leaves is even.