On Integer Additive Set-Indexers of Graphs

A set-indexer of a graph $G$ is an injective set-valued function $f:V(G) \rightarrow2^{X}$suchthatthefunction$f^{\oplus}:E(G)\rightarrow2^{X}-{\emptyset}$definedby$f^{\oplus}(uv) = f(u){\oplus} f(v)$forevery$uv{\in} E(G)$isalsoinjective,where$2^{X}$ is the set of all subsets of $X$ and $\oplus$ is the symmetric difference of sets. An integer additive set-indexer is defined as an injective function $f:V(G)\to 2^{{\mathbb{N}}_0}$ such that the induced function $g_f:E(G) \rightarrow 2^{$\mathbb{N}$_0}$definedby$g_f (uv) = f(u)+ f(v)$ is also injective. A graph $G$ which admits an IASI is called an IASI graph. An IASI $f$ is said to be a {\em weak IASI} if $\mathrm{\mid }{g}_f(uv)\mathrm{\mid }=max(\mathrm{\mid }f(u)\mathrm{\mid },\mathrm{\mid }f(v)\mathrm{\mid })$ and an IASI $f$ is said to be a {\em strong IASI} if $\mathrm{\mid }{g}_f(uv)\mathrm{\mid }=\mathrm{\mid }f(u)\mathrm{\mid }\mathrm{\mid }f(v)\mathrm{\mid }$ for all $u,v\in V(G)$. In this paper, we study about certain characteristics of inter additive set-indexers.