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(a,d)-Edge-Antimagic Total Labelings of Caterpillars

  • K. A. Sugeng
  • M. Miller
  • Slamin
  • M. Bača
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3330)

Abstract

For a graph G = (V,E), a bijection g from V(G) ∪ E(G) into { 1,2, ..., ∣ V(G) ∣ + ∣ E(G) ∣ } is called (a,d)-edge-antimagic total labeling of G if the edge-weights w(xy) = g(x) + g(y) + g(xy), xyE(G), form an arithmetic progression with initial term a and common difference d. An (a,d)-edge-antimagic total labeling g is called super (a,d)-edge-antimagic total if g(V(G)) = { 1,2,..., ∣ V(G) ∣ } .

We study super (a,d)-edge-antimagic total properties of stars S n and caterpillar S n1,n2,...,nr .

Keywords

Previous Theorem Arithmetic Progression Central Vertex Vertex Label Double Star 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • K. A. Sugeng
    • 1
  • M. Miller
    • 1
  • Slamin
    • 2
  • M. Bača
    • 3
  1. 1.School of Information Technology and Mathematical SciencesUniversity of BallaratAustralia
  2. 2.FKIPUniversitas JemberIndonesia
  3. 3.Department of Appl. MathematicsTechnical UniversityKošiceSlovak Republic

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