# The Sparing Number of the Cartesian Products of Certain Graphs

Source: [The Sparing Number of the Cartesian Products of Certain Graphs](<https://www.sota2.com/research/paper/68fa51111e209131ce970ab1>)

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

Data updated: 2025-10-25T11:12:25.688Z

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

Published: 2014-07-18T02:00:10.000Z

## Abstract

Let $\\mathbb{N}\_0$ be the set of all non-negative integers. An integer additive set-indexer (IASI) is defined as an injective function $f:V(G)\\rightarrow \\mathcal{P}(\\mathbb{N}\_0)$ such that the induced function $f^+:E(G) \\rightarrow \\mathcal{P}(\\mathbb{N}\_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$ and $\\mathcal{P}(\\mathbb{N}\_0)$ is the power set of $\\mathbb{N}\_0$. If $f^+(uv)=k \\forall ~ uv\\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexer. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer if $\|f^+(uv)\|=max(\|f(u)\|,\|f(v)\|) \\forall ~ uv\\in E(G)$. In this paper, we study about the sparing number of the cartesian product of two graphs.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1407.4869>)

[PDF](<https://arxiv.org/pdf/1407.4869.pdf>)