Acta Mathematica Sinica, English Series

, Volume 28, Issue 9, pp 1865–1874

Vertex-antimagic labelings of regular graphs

  • Ali Ahmad
  • Kashif Ali
  • Martin Bača
  • Petr Kovář
  • Andrea Semaničová-Feňovčíková
Article

DOI: 10.1007/s10114-012-1018-y

Cite this article as:
Ahmad, A., Ali, K., Bača, M. et al. Acta. Math. Sin.-English Ser. (2012) 28: 1865. doi:10.1007/s10114-012-1018-y
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Abstract

Let G = (V,E) be a finite, simple and undirected graph with p vertices and q edges. An (a, d)-vertex-antimagic total labeling of G is a bijection f from V (G) ∪ E(G) onto the set of consecutive integers 1, 2, …, p + q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f(x) assigned to the vertex x together with all values f(xy) assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices.

In this paper, we study the properties of such labelings and examine their existence for 2r-regular graphs when the difference d is 0, 1, …, r + 1.

Keywords

Super vertex-antimagic total labelingvertex-antimagic edge labelingregular graph

MR(2000) Subject Classification

05C78

Supplementary material

10114_2012_1018_MOESM1_ESM.eps (326 kb)
Supplementary material, approximately 325 KB.
10114_2012_1018_MOESM2_ESM.tex (35 kb)
Supplementary material, approximately 35.2 KB.

Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ali Ahmad
    • 1
  • Kashif Ali
    • 2
  • Martin Bača
    • 3
  • Petr Kovář
    • 4
  • Andrea Semaničová-Feňovčíková
    • 3
  1. 1.College of Computer Science and Information SystemsJazan UniversityJazanSaudi Arabia
  2. 2.Faculty of MathematicsCOMSATS Institute of Information TechnologyLahorePakistan
  3. 3.Department of Applied Mathematics and InformaticsTechnical UniversityKošiceSlovakia
  4. 4.Department of Applied MathematicsVŠB-Technical University of OstravaOstrava-PorubaCzech Republic