Acta Mathematica Sinica, English Series

, Volume 28, Issue 9, pp 1865-1874

First online:

Vertex-antimagic labelings of regular graphs

  • Ali AhmadAffiliated withCollege of Computer Science and Information Systems, Jazan University
  • , Kashif AliAffiliated withFaculty of Mathematics, COMSATS Institute of Information Technology
  • , Martin BačaAffiliated withDepartment of Applied Mathematics and Informatics, Technical University Email author 
  • , Petr KovářAffiliated withDepartment of Applied Mathematics, VŠB-Technical University of Ostrava
  • , Andrea Semaničová-FeňovčíkováAffiliated withDepartment of Applied Mathematics and Informatics, Technical University

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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 labeling vertex-antimagic edge labeling regular graph

MR(2000) Subject Classification