# On Integer Additive Set-Filtered Graphs

Source: [On Integer Additive Set-Filtered Graphs](<https://www.sota2.com/research/paper/68fa520f1e209131ce977e58>)

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

Data updated: 2025-10-25T11:41:12.792Z

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

Published: 2015-07-07T16:37:14.000Z

## 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-labeling (IASL) of a graph $G$ is an injective function $f:V(G)\\to \\mathcal{P}(\\mathbb{N}\_0)$ such that the induced function $f^+:E(G) \\to \\mathcal{P}(\\mathbb{N}\_0)$ is defined by $f^+ (uv) = f(u)+ f(v)$, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. In this paper, we introduce the notion of a particular type of integer additive set-indexers called integer additive set-filtered labeling of given graphs and study their characteristics.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1507.02173>)

[PDF](<https://arxiv.org/pdf/1507.02173.pdf>)