Vertex-Magic Total Labelings

Alison M. Marr and W. D. Wallis
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Alison M. Marr: Southwestern University, Department of Mathematics and Computer Science
W. D. Wallis: Southern Illinois University, Department of Mathematics

Chapter 3 in Magic Graphs, 2013, pp 71-109 from Springer

Abstract: Abstract A one-to-one map $$\lambda $$ from $$E(G) \cup V (G)$$ onto the integers $$\left \{1,2,\ldots,e + v\right \}$$ is a vertex-magic total labeling if there is a constant h so that for every vertex x, 3.1 $$\lambda (x) + \sum \lambda (xy) = h$$ where the sum is over all vertices y adjacent to x. So the magic requirement is wt(x) = h for all x. The constant h is called the magic constant for λ. Again, a graph with a vertex-magic total labeling will be called vertex-magic.

Keywords: Total Label; Constant Mag; Edge-magic Labeling; Magic Square; Largest Label (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-0-8176-8391-7_3

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