On integer additive set-filter 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 $f:V(G)\\to \\mathcal{P}(\\mathbb{N}_0)$ 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-filter labeling of given graphs and study their characteristics.