# Strong Integer Additive Set-valued Graphs: A Creative Review

Source: [Strong Integer Additive Set-valued Graphs: A Creative Review](<https://www.sota2.com/research/paper/68fa51ba1e209131ce975d52>)

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

Data updated: 2025-10-25T11:32:06.782Z

Authors: N. K. Sudev, K. A. Germina, K. P. Chithra

Published: 2015-04-23T10:20:08.000Z

## Abstract

For a non-empty ground set $X$, finite or infinite, the {\\em set-valuation} or {\\em set-labeling} of a given graph $G$ is an injective function $f:V(G) \\to \\mathcal{P}(X)$, where $\\mathcal{P}(X)$ is the power set of the set $X$. A set-indexer of a graph $G$ is an injective set-valued function $f:V(G) \\to \\mathcal{P}(X)$ such that the function $f^{\\ast}:E(G)\\to \\mathcal{P}(X)-\\{\\emptyset\\}$ defined by $f^{\\ast}(uv) = f(u){\\ast} f(v)$ for every $uv{\\in} E(G)$ is also injective., where $\\ast$ is a binary operation on sets. An integer additive set-indexer is defined as an injective function $f:V(G)\\to \\mathcal{P}({\\mathbb{N}\_0})$ such that the induced function $g\_f:E(G) \\to \\mathcal{P}(\\mathbb{N}\_0)$ defined by $g\_f (uv) = f(u)+ f(v)$ is also injective, where $\\mathbb{N}\_0$ is the set of all non-negative integers and $\\mathcal{P}(\\mathbb{N}\_0)$ is its power set. An IASI $f$ is said to be a strong IASI if $\|f^+(uv)\|=\|f(u)\|\\,\|f(v)\|$ for every pair of adjacent vertices $u,v$ in $G$. In this paper, we critically and creatively review the concepts and properties of strong integer additive set-valued graphs.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1504.07132>)

[PDF](<https://arxiv.org/pdf/1504.07132.pdf>)