Edge-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 2 in Magic Graphs, 2013, pp 15-69 from Springer

Abstract: Abstract An edge-magic total labeling on a graph G is a one-to-one map λ from $$ V (G) \ cup E(G) $$ onto the integers 1,2, …, v + e, where v = | V (G) | and e = | E(G) |, with the property that, given any edge xy, $$\lambda (x) + \lambda (xy) + \lambda (y) = k$$ for some constant k. In other words, wt(xy) = k for any choice of edge xy. Then k is called the magic sum of G. Any graph with an edge-magic total labeling will be called edge-magic. described.

Keywords: Magic Sum; Super Edge-magic Labelings; Sidon Sequence; Vertex Labels; Magical Strength (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-0-8176-8391-7_2

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