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A Characterisation of Strong Integer Additive Set-Indexers of Graphs (1402.0826v1)

Published 4 Feb 2014 in math.CO

Abstract: 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 strong integer additive set-indexer if $|g_f(uv)|=|f(u)|.|f(v)|~\forall ~ uv\in E(G)$. We already have some characteristics of the graphs which admit strong integer additive set-indexers. In this paper, we study the characteristics of certain graph classes, graph operations and graph products that admit strong integer additive set-indexers.

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