A Study on Arithmetic Integer Additive Set-Indexers of Graphs

Sudev Naduvath

Abstract


Let $\N$ be the set of all non-negative integers and $\cP(\N)$ be its power set. An integer additive set-indexer (IASI) of a graph $G$ is an injective function $f:V(G)\to \cP(\N)$ such that the induced function $f^+:E(G) \to \cP(\N)$ defined by $f^+ (uv) = f(u)+ f(v)$ 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 $|f^+(uv)|=\max(|f(u)|,|f(v)|)$ and an IASI $f$ is said to be a {\em strong IASI} if $|f^+(uv)|=|f(u)|\,|f(v)|$ for all $uv\in E(G)$. In this paper, we introduce the notion of arithmetic integer additive set-indexers of a given graph $G$ as an IASI with respect to which all elements of $G$ have arithmetic progressions as their set-labels and study the characteristics of this type of IASIs.

Keywords


Integer additive set-indexers; set-indexing number; arithmetic integer additive set-indexers; deterministic index; deterministic ratio.

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DOI: http://dx.doi.org/10.26713%2Fjims.v10i1-2.617

eISSN 0975-5748; pISSN 0974-875X