  An integer additive set-indexer is defined as an injective function
$f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $g_f:E(G)
\rightarrow 2^{\mathbb{N}_0}$ defined by $g_f (uv) = f(u)+ f(v)$ is also
injective, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. If $g_f(uv)=k
\forall uv\in E(G)$, then $f$ is said to be a $k$-uniform integer additive
set-indexers. An integer additive set-indexer $f$ is said to be a weak integer
additive set-indexer if $|g_f(uv)|=max(|f(u)|,|f(v)|) \forall uv\in E(G)$. We
have some characteristics of the graphs which admit weak integer additive
set-indexers. We already have some results on the admissibility of weak integer
additive set-indexer by certain graphs and finite graph operations. In this
paper, we study further characteristics of certain graph products like
cartesian product and corona of two weak IASI graphs and their admissibility of
weak integer additive set-indexers and provide some useful results on these
types of set-indexers.
