Totally magic graphs

A total labeling of a graph with v vertices and e edges is defined as a one-to-one map taking the vertices and edges onto the integers 1,2,…, v+ e. Such a labeling is vertex magic if the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vert...

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Bibliographic Details
Published in:Discrete mathematics 2002-06, Vol.254 (1), p.103-113
Main Authors: Exoo, Geoffrey, Ling, Alan C.H., McSorley, John P., Phillips, N.C.K., Wallis, W.D.
Format: Article
Language:English
Subjects:
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science
control theory
systems
Exact sciences and technology
Graph labeling
Graph theory
Information retrieval. Graph
Magic graph
Mathematics
Sciences and techniques of general use
Theoretical computing
Valuation
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Summary:A total labeling of a graph with v vertices and e edges is defined as a one-to-one map taking the vertices and edges onto the integers 1,2,…, v+ e. Such a labeling is vertex magic if the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex, and edge magic if the sum of an edge label and the labels of the endpoints of the edge is constant. In this paper we examine graphs possessing a labeling that is simultaneously vertex magic and edge magic. Such graphs appear to be rare.
ISSN:0012-365X
1872-681X
DOI:10.1016/S0012-365X(01)00367-3