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Edge-Magic Total Labelings

In: Magic Graphs

Author

Listed:
  • Alison M. Marr

    (Southwestern University, Department of Mathematics and Computer Science)

  • W. D. Wallis

    (Southern Illinois University, Department of Mathematics)

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.

Suggested Citation

  • Alison M. Marr & W. D. Wallis, 2013. "Edge-Magic Total Labelings," Springer Books, in: Magic Graphs, edition 2, chapter 2, pages 15-69, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-8391-7_2
    DOI: 10.1007/978-0-8176-8391-7_2
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