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For a non-empty ground set $X$, finite or infinite, the {\em set-valuation}or {\em set-labeling} of a given graph $G$ is an injective function $f:V(G) \to\mathcal{P}(X)$, where $\mathcal{P}(X)$ is the power set of the set $X$. Aset-indexer of a graph $G$ is an injective set-valued function $f:V(G) \to\mathcal{P}(X)$ such that the function $f^{\ast}:E(G)\to\mathcal{P}(X)-\{\emptyset\}$ defined by $f^{\ast}(uv) = f(u){\ast} f(v)$ forevery $uv{\in} E(G)$ is also injective., where $\ast$ is a binary operation onsets. An integer additive set-indexer is defined as an injective function$f:V(G)\to \mathcal{P}({\mathbb{N}_0})$ such that the induced function$g_f:E(G) \to \mathcal{P}(\mathbb{N}_0)$ defined by $g_f (uv) = f(u)+ f(v)$ isalso injective, where $\mathbb{N}_0$ is the set of all non-negative integersand $\mathcal{P}(\mathbb{N}_0)$ is its power set. An IASI $f$ is said to be astrong IASI if $|f^+(uv)|=|f(u)|\,|f(v)|$ for every pair of adjacent vertices$u,v$ in $G$. In this paper, we critically and creatively review the conceptsand properties of strong integer additive set-valued graphs.

Strong Integer Additive Set-valued Graphs: A Creative Review