On Integer Additive Set-Filtered Graphs

TL;DR

This paper introduces and studies a new class of graph labelings called integer additive set-filtered labelings, exploring their properties and characteristics within the framework of integer additive set-labelings.

Contribution

It defines the concept of integer additive set-filtered labelings and investigates their properties, expanding the theory of integer additive set-labelings.

Findings

Characterization of integer additive set-filtered labelings

Conditions for existence of such labelings in graphs

Properties and structural features of these labelings

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.