Coloring vertices and edges of a graph by nonempty subsets of a set

A graph G is strongly set colorable if V ( G ) ∪ E ( G ) can be assigned distinct nonempty subsets of a set of order n , where | V ( G ) | + | E ( G ) | = 2 n − 1 , such that each edge is assigned the symmetric difference of its end vertices. We prove results about strongly set colorability of graphs (they are related to a conjecture of S.M. Hegde.) We also prove another conjecture of Hegde on a related type of set coloring of complete bipartite graphs.