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Acharya introduced the notion of set-valuations of graphs as a set analogue of the number valuations of graphs. Also we have the notion of set-indexers, integer additive set-indexers and k-uniform integer additive set-indexers. In this paper, we initiate a study of the graphs which admit k-uniform integer additive set-indexers as a generalisation to the earlier studies of 1-uniform and 2-uniform integer additive set-indexers. We introduce the notion of weakly uniform integer additivedoi:10.12988/imf.2013.310188 fatcat:n3s6bifzwrdx7mow2nja6idxmu