# Weak Integer Additive Set-Indexers of Certain Graph Operations

Source: [Weak Integer Additive Set-Indexers of Certain Graph Operations](<https://www.sota2.com/research/paper/68fa50cc1e209131ce96e833>)

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

Data updated: 2025-10-25T11:03:34.853Z

Authors: N K Sudev, K A Germina

Published: 2013-10-23T02:00:14.000Z

## 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, where $f(u)+f(v)$ is the sum set of $f(u)$ and $f(v)$ and $\\mathbb{N}\_0$ is the set of all non-negative integers. If $g\_f(uv)=k \\forall uv\\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexers. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer if $\|g\_f(uv)\|=max(\|f(u)\|,\|f(v)\|) \\forall uv\\in E(G)$. A weak integer additive set-indexer $f$ is called a weakly $k$-uniform integer additive set-indexer if $g\_f(e)=k \\forall  e\\in E(G)$. We have some characteristics of the graphs which admit weak and weakly uniform integer additive set-indexers. In this paper, we study the admissibility of weak integer additive set-indexer by certain graphs and finite graph operations.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1310.6091>)

[PDF](<https://arxiv.org/pdf/1310.6091.pdf>)