# A Characterisation of Strong Integer Additive Set-Indexers of Graphs

Source: [A Characterisation of Strong Integer Additive Set-Indexers of Graphs](<https://www.sota2.com/research/paper/68fa519f1e209131ce975097>)

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: 2014-02-04T18:45:15.000Z

## 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-indexers. An integer additive set-indexer $f$ is said to be a strong integer additive set-indexer if $\|g\_f(uv)\|=\|f(u)\|.\|f(v)\|~\\forall ~ uv\\in E(G)$. We already have some characteristics of the graphs which admit strong integer additive set-indexers. In this paper, we study the characteristics of certain graph classes, graph operations and graph products that admit strong integer additive set-indexers.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1402.0826>)

[PDF](<https://arxiv.org/pdf/1402.0826.pdf>)