# A Study on Integer Additive Set-Valuations of Signed Graphs

Source: [A Study on Integer Additive Set-Valuations of Signed Graphs](<https://www.sota2.com/research/paper/68fa524f1e209131ce97a09f>)

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

Data updated: 2025-10-25T11:50:05.244Z

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

Published: 2015-11-01T01:49:31.000Z

## Abstract

Let $\\N$ denote the set of all non-negative integers and $\\cP(\\N)$ be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective set-valued function $f:V(G)\\to \\cP(\\N)-\\{\\emptyset\\}$ such that the induced function $f^+:E(G) \\to \\cP(\\N)-\\{\\emptyset\\}$ is defined by $f^+ (uv) = f(u)+ f(v)$, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. A graph which admits an IASL is usually called an IASL-graph. An IASL $f$ of a graph $G$ is said to be an integer additive set-indexer (IASI) of $G$ if the associated function $f^+$ is also injective. In this paper, we define the notion of integer additive set-labeling of signed graphs and discuss certain properties of signed graphs which admits certain types of integer additive set-labelings.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1511.00678>)

[PDF](<https://arxiv.org/pdf/1511.00678.pdf>)