Edge-magic group labellings of countable graphs
type: Item
instance of: scholarly article
title: Edge-magic group labellings of countable graphs
zbMATH Open document ID: 1111.05085
author: D. Combe
author: Adrian M. Nelson
author: Nicholas J. Cavenagh
published in: The Electronic Journal of Combinatorics
publication date: 2007-03-12T00:00:00Z
full work available at URL: https://eudml.org/doc/127272
full work available at URL: v13i1r92.html
review text: Summary: We investigate the existence of edge-magic labellings of countably infinite graphs by abelian groups. We show that for a large class of abelian groups, including the integers \(\mathbb{Z}\), there is such a labelling whenever the graph has an infinite set of disjoint edges. A graph without an infinite set of disjoint edges must be some subgraph of \(H + \mathcal I\), where \(H\) is some finite graph and \(\mathcal T\) is a countable set of isolated vertices. Using power series of rational functions, we show that any edge-magic \(\mathbb Z\)-labelling of \(H + \mathcal I\) has almost all vertex labels making up pairs of half-modulus classes. We also classify all possible edge-magic \(\mathbb Z\)-labellings of \(H + \mathcal I\) under the assumption that the vertices of the finite graph are labelled consecutively.
Mathematics Subject Classification ID: 05C78
zbMATH DE Number: 5132805
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5132805