Acta Mathematica Sinica, English Series

, Volume 28, Issue 9, pp 1865–1874

Vertex-antimagic labelings of regular graphs


  • Ali Ahmad
    • College of Computer Science and Information SystemsJazan University
  • Kashif Ali
    • Faculty of MathematicsCOMSATS Institute of Information Technology
    • Department of Applied Mathematics and InformaticsTechnical University
  • Petr Kovář
    • Department of Applied MathematicsVŠB-Technical University of Ostrava
  • Andrea Semaničová-Feňovčíková
    • Department of Applied Mathematics and InformaticsTechnical University

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


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.


Super vertex-antimagic total labelingvertex-antimagic edge labelingregular graph

MR(2000) Subject Classification

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