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

A graph GG is strongly set colorable if V(G)∪E(G)V(G)∪E(G) can be assigned distinct nonempty subsets of a set of order nn, where |V(G)|+|E(G)|=2n−1|V(G)|+|E(G)|=2n−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.