# The Sparing Number of Certain Graph Powers

Source: [The Sparing Number of Certain Graph Powers](<https://www.sota2.com/research/paper/68fa52111e209131ce978192>)

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

Data updated: 2025-10-25T11:42:13.648Z

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

Published: 2014-05-14T17:12:23.000Z

## Abstract

An integer additive set-indexer is defined as an injective function $f:V(G)\\rightarrow 2^{\\mathbb{N}\_0}$ such that the induced function $g\_f:E(G) \\rightarrow 2^{\\mathbb{N}\_0}$ defined by $g\_f (uv) = f(u)+ f(v)$ is also injective. An IASI $f$ is said to be a weak IASI if $\|g\_f(uv)\|=max(\|f(u)\|,\|f(v)\|)$ for all $u,v\\in V(G)$. A graph which admits a weak IASI may be called a weak IASI graph. The set-indexing number of an element of a graph $G$, a vertex or an edge, is the cardinality of its set-labels. The sparing number of a graph $G$ is the minimum number of edges with singleton set-labels, required for a graph $G$ to admit a weak IASI. In this paper, we study the admissibility of weak IASI by certain graph powers and their sparing numbers.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1405.4787>)

[PDF](<https://arxiv.org/pdf/1405.4787.pdf>)