# On the Sparing Number of the Edge-Corona of Graphs

Source: [On the Sparing Number of the Edge-Corona of Graphs](<https://www.sota2.com/research/paper/68fa51d71e209131ce976bda>)

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

Data updated: 2025-10-25T11:36:09.206Z

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

Published: 2015-05-19T02:37:25.000Z

## Abstract

Let $\\mathbb{N}\_0$ be the set of all non-negative integers and $\\mathcal{P}(\\mathbb{N}\_0)$ be its the power set. An integer additive set-indexer (IASI) of a graph $G$ is an injective function $f:V(G)\\to \\mathcal{P}(\\mathbb{N}\_0)$ such that the induced function $f^+:E(G) \\to \\mathcal{P}(\\mathbb{N}\_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective, where $f(u)+f(v)$ is the sum set of $f(u)$ and $f(v)$. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer (weak IASI) if $\|f^+(uv)\|=\\max(\|f(u)\|,\|f(v)\|)~\\forall ~ uv\\in E(G)$. The minimum number of singleton set-labeled edges required for the graph $G$ to admit an IASI is called the sparing number of the graph. In this paper, we discuss the admissibility of weak IASI by a particular type of graph product called the edge corona of two given graphs and determine the sparing number of the edge corona of certain graphs.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1505.04854>)

[PDF](<https://arxiv.org/pdf/1505.04854.pdf>)