# Some New Results on Integer Additive Set-Valued Signed Graphs

Source: [Some New Results on Integer Additive Set-Valued Signed Graphs](<https://www.sota2.com/research/paper/68fa53171e209131ce9802a1>)

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

Data updated: 2025-10-25T12:15:05.691Z

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

Published: 2016-09-01T16:05:23.000Z

## Abstract

Let $X$ denotes a set of non-negative integers and $\\mathscr{P}(X)$ be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective set-valued function $f:V(G)\\to \\mathscr{P}(X)-\\{\\emptyset\\}$ such that the induced function $f^+:E(G) \\to \\mathscr{P}(X)-\\{\\emptyset\\}$ is defined by $f^+(uv)=f(u)+f(v);\\ \\forall\\, uv\\in E(G)$, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. An IASL of a signed graph is an IASL of its underlying graph $G$ together with the signature $\\sigma$ defined by $\\sigma(uv)=(-1)^{\|f^+(uv)\|};\\ \\forall\\, uv\\in E(\\Sigma)$. In this paper, we discuss certain characteristics of the signed graphs which admits certain types of integer additive set-labelings.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1609.00295>)

[PDF](<https://arxiv.org/pdf/1609.00295.pdf>)