Totally magic graphs
type: Item
instance of: scholarly article
title: Totally magic graphs
zbMATH Open document ID: 0995.05129
DOI: 10.1016/S0012-365X(01)00367-3
author: Geoffrey Exoo
author: Alan C. H. Ling
author: J. P. McSorley
author: N. C. K. Phillips
author: Walter D. Wallis
published in: Discrete Mathematics
publication date: 2002-08-29T00:00:00Z
review text: A one-to-one mapping \(V\cup E \rightarrow \{1, 2, \ldots, |V|+|E|\}\) is vertex magic, if each vertex has the same sum of its label and the labels of its incident edges, and is edge magic if each edge has the same sum of its label and the labels of its endpoints. This paper investigates graphs that have a labelling that is both vertex magic and edge magic, i.e., totally magic. It appears that few graphs have such a labelling. The paper gives a number of necessary conditions, and a number of graphs with a totally magic labelling. Also, with help of computer analysis, the list all such graphs with up to 10 vertices is given.
Mathematics Subject Classification ID: 05C78
zbMATH DE Number: 1792453
zbMATH Keywords: graph labelling
zbMATH Keywords: totally magic graphs
reviewed by: Hans L. Bodlaender
describes a project that uses: nauty
MaRDI profile type: Publication
full work available at URL: s0012-365x(01)00367-3
OpenAlex ID: W2007032991
description: scientific article; zbMATH DE number 1792453