  We settle affirmatively a conjecture posed in [S. M. Hegde, Set colorings of
graphs, European Journal of Combinatorics 30 (4) (2009), 986--995]: If some
subsets of a set X are assigned injectively to all vertices of a complete
bipartite graph G such that the collection of all sets, each of which is the
symmetric difference of the sets assigned to the ends of some edge, is the set
of all nonempty subsets of X, then G is a star.
