An integer additive set-indexer is defined as an injective function  such that the induced function  defined by  is also injective. An IASI f is said to be a weak IASI if  for all  A graph which admits a weak IASI may be called a weak IASI graph. The set-indexing number of an element of a graph G, a vertex or an edge, is the cardinality of its set-labels. The sparing number of a graph G is the minimum number of edges with singleton set-labels, required for a graph G to admit a weak IASI . In this paper, we study about the sparing number of certain graphs and the relation of sparing number with some other parameters like matching number, chromatic number, covering number, independence number, etc.

weak integer additive set-indexers, mono-indexed elements of a graph, sparing number of a graph.