Research article

Introduction for SuperHyperGraph Labeling and MultiLabeling

Abstract

A finite hypergraph generalizes the classical graph model by allowing hyperedges that can connect any nonempty subset of vertices. Building on this foundation, a finite SuperHyperGraph is obtained through iterative application of the powerset construction, thereby creating nested families of vertex and edge sets that capture multi-layered relationships. Graph labeling assigns numbers or symbols to vertices and/or edges of a graph under rules, modeling constraints, optimization, or communication. In this paper, we define and study the mathematical properties of Graph Labeling, HyperGraph Labeling, SuperHyper- Graph Labeling, Graph MultiLabeling, HyperGraph MultiLabeling, and SuperHyperGraph MultiLabeling.