# A Study on Prime Arithmetic Integer Additive Set-Indexers of Graphs

Source: [A Study on Prime Arithmetic Integer Additive Set-Indexers of Graphs](<https://www.sota2.com/research/paper/68fa51121e209131ce970b1b>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T11:12:25.688Z

Authors: N. K. Sudev, K. A. Germina

Published: 2014-07-09T01:57:10.000Z

## Abstract

Let $\\mathbb{N}\_0$ be the set of all non-negative integers and $\\mathcal{P}(\\mathbb{N}\_0)$ be its power set. An integer additive set-indexer (IASI) is defined as an injective function $f:V(G)\\to \\mathcal{P}(\\mathbb{N}\_0)$ such that the induced function $f^+:E(G) \\to \\mathcal{P}(\\mathbb{N}\_0)$ defined by $f^+(uv) = f(u)+ f(v)$ is also injective, where $\\mathbb{N}\_0$ is the set of all non-negative integers. A graph $G$ which admits an IASI is called an IASI graph. An IASI of a graph $G$ is said to be an arithmetic IASI if the elements of the set-labels of all vertices and edges of $G$ are in arithmetic progressions. In this paper, we discuss about a particular type of arithmetic IASI called prime arithmetic IASI.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1407.4676>)

[PDF](<https://arxiv.org/pdf/1407.4676.pdf>)