# A Study on Integer Additive Set-Graceful Graphs

Source: [A Study on Integer Additive Set-Graceful Graphs](<https://www.sota2.com/research/paper/68fa523d1e209131ce979916>)

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

Data updated: 2025-10-25T11:48:10.628Z

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

Published: 2014-03-17T01:59:43.000Z

## Abstract

A set-labeling of a graph $G$ is an injective function $f:V(G)\\to \\mathcal{P}(X)$, where $X$ is a finite set and a set-indexer of $G$ is a set-labeling such that the induced function $f^{\\oplus}:E(G)\\rightarrow \\mathcal{P}(X)-\\{\\emptyset\\}$ defined by $f^{\\oplus}(uv) = f(u){\\oplus}f(v)$ for every $uv{\\in} E(G)$ is also injective. An integer additive set-labeling is an injective function $f:V(G)\\rightarrow \\mathcal{P}(\\mathbb{N}\_0)$, $\\mathbb{N}\_0$ is the set of all non-negative integers and an integer additive set-indexer is an integer additive set-labeling such that the induced function $f^+:E(G) \\rightarrow \\mathcal{P}(\\mathbb{N}\_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective. In this paper, we extend the concepts of set-graceful labeling to integer additive set-labelings of graphs and provide some results on them.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1403.3984>)

[PDF](<https://arxiv.org/pdf/1403.3984.pdf>)