A Study on Arithmetic Integer Additive Set-Indexers of Graphs

Authors

  • Sudev Naduvath Vidya Academy of Science & Technology, Thrissur, India

DOI:

https://doi.org/10.26713/jims.v10i1-2.617

Keywords:

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

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.

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Published

2018-08-10
CITATION

How to Cite

Naduvath, S. (2018). A Study on Arithmetic Integer Additive Set-Indexers of Graphs. Journal of Informatics and Mathematical Sciences, 10(1-2), 321–332. https://doi.org/10.26713/jims.v10i1-2.617

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Section

Research Articles