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An integer additive set-indexer is said to be $k$-uniform if $|g_f(uv)|=k$ for all $u,v\\in V(G)$. An integer additive set-indexer $f$ is said to be a weak IASI if $|g_f(uv)|=max(|f(u)|,|f(v)|)$ for all $u,v\\in V(G)$. 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