On the Sparing Number of the Edge-Corona of Graphs

K. P. Chithra; K. A. Germina; N. K. Sudev

doi:10.5120/20706-3025

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arXiv · 1505.04854

On the Sparing Number of the Edge-Corona of Graphs

K. P. Chithra·K. A. Germina·N. K. Sudev

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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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K. P. Chithra, K. A. Germina, N. K. Sudev. 2015-05-19. On the Sparing Number of the Edge-Corona of Graphs. https://doi.org/10.5120/20706-3025

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