Set-Valuations of Graphs and their Applications: A Survey (original) (raw)

f is injective (uniform) then the set M is a DPD-set (ODPU-set) of G and G is a DPD-graph (ODPU-graph). Following a suggestion made by Michel Deza, Acharya and Germina, who had been studying topological set-valuations, introduced the particular kind of set-valuations for which a metric, especial ly the cardinality of the symmetric difference, is associated with each pair of vertice s in proportion to the distance between them in the graph. Particular cases of set-valuatio ns of graphs are also being studied in detail by many authors. In this paper, we give a br ief report of the existing results, new challenges, open problems and conjectures that are abound in this area of set-valuations of graphs.