On Integer Additive Set-Indexers of Graphs

Abstract

A set-indexer of a graph $G$ is an injective set-valued function $f:V(G)\to 2^X$ such that the function $f^{\oplus }:E(G)\to 2^X-\{\varnothing \}$ defined by $f^{\oplus }(uv)=f(u)\oplus f(v)$ for every $uv\in E(G)$ is also injective, where $2^X$ is the set of all subsets of $X$ and $\oplus$ is the symmetric difference of sets. An integer additive set-indexer is defined as an injective function $f:V(G)\to 2^{{\mathbb{N}}_0}$ such that the induced function $g_f:E(G)\to 2^{{\mathbb{N}}_0}$ defined by $g_f(uv)=f(u)+f(v)$ is also injective. A graph $G$ which admits an IASI is called an IASI graph. An IASI $f$ is said to be a {\em weak IASI} if $|g_f(uv)|=max(|f(u)|,|f(v)|)$ and an IASI $f$ is said to be a {\em strong IASI} if $|g_f(uv)|=|f(u)||f(v)|$ for all $u,v\in V(G)$. In this paper, we study about certain characteristics of inter additive set-indexers.

12 pages. arXiv admin note: text overlap with arXiv:1312.7674 To Appear in Int. J. Math. Sci.& Engg. Appl. in March 2014

References in corpus (2)

• On Weakly Uniform Integer Additive Set-Indexers of Graphs
• A Characterisation of Weak Integer Additive Set-Indexers of Graphs

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