# Further Studies on the Sparing Number of Graphs

Source: [Further Studies on the Sparing Number of Graphs](<https://www.sota2.com/research/paper/68fa513c1e209131ce971ede>)

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

Data updated: 2025-10-25T11:17:29.523Z

Authors: N K Sudev, K A Germina

Published: 2014-08-13T18:15:56.000Z

## Abstract

Let $\\mathbb{N}\_0$ denote the set of all non-negative integers and $\\mathcal{P}(\\mathbb{N}\_0)$ be its power set. An integer additive set-indexer is 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 $f(u)+f(v)$ is the sum set of $f(u)$ and $f(v)$. If $f^+(uv)=k~\\forall~uv\\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexer. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer if $\|f^+(uv)\|=\\max(\|f(u)\|,\|f(v)\|)~\\forall ~ uv\\in E(G)$. In this paper, we study the admissibility of weak integer additive set-indexer by certain graphs and graph operations.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1408.3074>)

[PDF](<https://arxiv.org/pdf/1408.3074.pdf>)