Magic labelings of graphs
type: Item
instance of: scholarly article
zbMATH Open document ID: 0977.05115
publication date: 2001-12-17T00:00:00Z
Mathematics Subject Classification ID: 05C78
zbMATH DE Number: 1682902
zbMATH Keywords: magic labeling
zbMATH Keywords: vertex cycle cover
MaRDI profile type: Publication
author: F. Göbel
author: C. Hoede
title: Magic labelings of graphs
published in: Ars Combinatoria
review text: The authors investigate such integer labelings \(w\) (called ``magic'') of edges of a graph \(G\), in which \(\sum_{v\in e}w(e)\) is a constant \(s\) independent of the vertex \(v\). They introduce basis graphs of type I and II. For the type I a unique, up to a constant factor, labeling exists with \(s>0\) and no \(0\) label. For the type II the same labeling exists but with \(s=0\). Basis graphs of both types are characterized. An algorithm reducing the problem of finding positive labelings to an integer programming problem is presented. A connection to vertex cycle covers is discussed.
reviewed by: Martin Klazar
description: scientific article; zbMATH DE number 1682902