# A Study on Semi-arithmetic Integer Additive Set-Indexers of Graphs

Source: [A Study on Semi-arithmetic Integer Additive Set-Indexers of Graphs](<https://www.sota2.com/research/paper/68fa50f71e209131ce96fa12>)

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

Data updated: 2025-10-25T11:08:29.811Z

Authors: N K Sudev, K A Germina

Published: 2014-03-25T17:53:57.000Z

## Abstract

An integer additive set-indexer is defined as an injective function $f:V(G)\\rightarrow 2^{\\mathbb{N}\_0}$ such that the induced function $g\_f:E(G) \\rightarrow 2^{\\mathbb{N}\_0}$ defined by $g\_f (uv) = f(u)+ f(v)$ is also injective. An integer additive set-indexer $f$ is said to be an arithmetic integer additive set-indexer if every element of $G$ are labeled by non-empty sets of non negative integers, which are in arithmetic progressions. An integer additive set-indexer $f$ is said to be a semi-arithmetic integer additive set-indexer if vertices of $G$ are labeled by non-empty sets of non negative integers, which are in arithmetic progressions, but edges are not labeled by non-empty sets of non negative integers, which are in arithmetic progressions. In this paper, we discuss about semi-arithmetic integer additive set-indexer and establish some results on this type of integer additive set-indexers.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1403.6435>)

[PDF](<https://arxiv.org/pdf/1403.6435.pdf>)