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arXiv · 1310.5779

A Characterisation of Weak Integer Additive Set-Indexers of Graphs

N K Sudev·K A Germina
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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. An integer additive set-indexer is said to be $k$-uniform if $|g_f(e)| = k$ for all $e\in E(G)$. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer if $|g_f(uv)|=max(|f(u)|,|f(v)|)$ for all $u,v\in V(G)$. In this paper, we study the characteristics of certain graphs and graph classes which admit weak integer additive set-indexers.

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N K Sudev, K A Germina. 2013-10-22. A Characterisation of Weak Integer Additive Set-Indexers of Graphs. https://doi.org/10.5899/2014/jfsva-00189

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