# A Study on the Nourishing Number of Graphs and Graph Powers

Source: [A Study on the Nourishing Number of Graphs and Graph Powers](<https://www.sota2.com/research/paper/68fa519f1e209131ce97509f>)

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

Data updated: 2025-10-25T11:29:14.401Z

Authors: N K Sudev, K A Germina

Published: 2014-05-14T17:00:22.000Z

## 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 sumset of $f(u)$ and $f(v)$. If $g\_f(uv)=k~\\forall~uv\\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexer. An integer additive set-indexer $f$ is said to be a strong integer additive set-indexer if $\|g\_f(uv)\|=\|f(u)\|.\|f(v)\|~\\forall ~ uv\\in E(G)$. In this paper, we study the characteristics of certain graph classes and graph powers that admit strong integer additive set-indexers.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1405.4788>)

[PDF](<https://arxiv.org/pdf/1405.4788.pdf>)