# A Study on Set-Valuations of Signed Graphs

Source: [A Study on Set-Valuations of Signed Graphs](<https://www.sota2.com/research/paper/68fa53341e209131ce9816cf>)

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

Data updated: 2025-10-25T12:19:08.769Z

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

Published: 2016-10-01T08:20:36.000Z

## Abstract

Let $X$ be a non-empty ground set and $\\mathcal{P}(X)$ be its power set. A set-labeling (or a set-valuation) of a graph $G$ is an injective set-valued function $f:V(G)\\to \\mathcal{P}(X)$ such that the induced function $f^\\oplus:E(G) \\to \\mathcal{P}(X)$ is defined by $f^\\oplus(uv) = f(u)\\oplus f(v)$, where $f(u)\\oplus f(v)$ is the symmetric difference of the sets $f(u)$ and $f(v)$. A graph which admits a set-labeling is known to be a set-labeled graph. A set-labeling $f$ of a graph $G$ is said to be a set-indexer of $G$ if the associated function $f^\\oplus$ is also injective. In this paper, we define the notion of set-valuations of signed graphs and discuss certain properties of signed graphs which admits certain types of set-valuations.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1610.00698>)

[PDF](<https://arxiv.org/pdf/1610.00698.pdf>)