A Characterisation of weak integer additive Set-Indexers of graphs

An integer additive set-indexer is defined as an injective function f : V(G) → 2 N0 such that the induced function gf : E(G) → 2 N0 defined by gf(uv) = f(u)+ f(v) is also injective. An integer additive set-indexer is said to be k-uniform if |gf(e)| = k for all e ∈ E(G). An integer additive set-indexer f is said to be a weak integer additive set-indexer if |gf(uv)| = max(|f(u)|; |f(v)|) for all u;v ∈V(G). In this paper, we study the characteristics of certain graphs and graph classes which admit weak integer additive set-indexers.