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arXiv · 1507.02173

On Integer Additive Set-Filtered Graphs

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

Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ is defined by $f^+ (uv) = f(u)+ f(v)$, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. In this paper, we introduce the notion of a particular type of integer additive set-indexers called integer additive set-filtered labeling of given graphs and study their characteristics.

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N. K. Sudev, K. P. Chithra, K. A. Germina. 2015-07-07. On Integer Additive Set-Filtered Graphs. https://arxiv.org/abs/1507.02173

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