# A Note on Sparing Number Algorithm of Graphs

Source: [A Note on Sparing Number Algorithm of Graphs](<https://www.sota2.com/research/paper/68fa52681e209131ce97ae1c>)

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

Data updated: 2025-10-25T11:52:59.839Z

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

Published: 2015-12-02T10:53:08.000Z

## Abstract

Let $X$ denote a set of all non-negative integers and $\\sP(X)$ be its power set. A weak integer additive set-labeling (WIASL) of a graph $G$ is an injective set-valued function $f:V(G)\\to \\sP(X)-\\{\\emptyset\\}$ where induced function $f^+:E(G) \\to \\sP(X)-\\{\\emptyset\\}$ is defined by $f^+ (uv) = f(u)+ f(v)$ such that either $\|f^+ (uv)\|=\|f(u)\|$ or $\|f^+ (uv)\|=\|f(v)\|$ , where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. The sparing number of a WIASL-graph $G$ is the minimum required number of edges in $G$ having singleton set-labels. In this paper, we discuss an algorithm for finding the sparing number of arbitrary graphs.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1512.01113>)

[PDF](<https://arxiv.org/pdf/1512.01113.pdf>)