On Integer Additive Set-Filtered Graphs

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)$suchthattheinducedfunction$f^+:E(G) \to $\mathcal{P}$($\mathbb{N}$_0)$isdefinedby$f^+ (uv) = f(u)+ f(v)$,where$f(u)+f(v)$isthesumsetof$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.