Set-Magic Labelings of Infinite Graphs

Abstract

A graph \(G\) without isolated vertices is said to be set-magic if its edges can be assigned distinct subsets of a set \(X\) such that for every vertex \(v\) of \(G\), the union of the subsets assigned to the edges incident with \(v\) is \(X\); such a set-assignment is called a set-magic labeling of \(G\). In this note, we study infinite set-magic graphs and characterize infinite graphs \(G\) having set-magic labelings \(f\) such that \(|f(e)| = 2\) for all \(e \in E(G)\).