# A Study on Arithmetic Integer Additive Set-Indexers of Graphs Source: [A Study on Arithmetic Integer Additive Set-Indexers of Graphs]() Collection index: [llms.txt]() Data updated: 2025-10-25T11:04:35.546Z Authors: N. K. Sudev, K. A. Germina Published: 2013-12-30T10:50:12.000Z ## Abstract A set-indexer of a graph $G$ is an injective set-valued function $f:V(G) \\rightarrow2^{X}$ such that the function $f^{\\oplus}:E(G)\\rightarrow2^{X}-\\{\\emptyset\\}$ 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 $f:V(G)\\rightarrow 2^{\\mathbb{N}\_0}$ such that the induced function $f^+:E(G) \\rightarrow 2^{\\mathbb{N}\_0}$ 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 weak IASI if $\|f^+(uv)\|=max(\|f(u)\|,\|f(v)\|)$ and an IASI $f$ is said to be a strong IASI if $\|f^+(uv)\|=\|f(u)\| \|f(v)\|$ for all $u,v\\in V(G)$. In this paper, we discuss about a special type of integer additive set-indexers called arithmetic integer additive set-indexer and establish some results on this type of integer additive set-indexers. We also check the admissibility of arithmetic integer additive set-indexer by certain graphs associated with a given graph. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()