On Integer Additive Set-Filtered Graphs

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.

12 Pages, 4 figures, Submitted

References in corpus (2)

• On Integer Additive set-Sequential Graphs
• A Creative Review on Integer Additive Set-Valued Graphs