Generation of Anti-Magic Graphs

Muthukkumar, S.; Rajendran, K.

doi:10.28924/2291-8639-23-2025-30

Research Article

Generation of Anti-Magic Graphs

S. Muthukkumar
K. Rajendran*

* Corresponding author

Abstract

An anti-magic labeling of a graph G is a one-to-one correspondence between E(G) and {1, 2, · · ·, |E|} such that the vertex-sum for distinct vertices are different. Vertex-sum of a vertex u ∈ V(G) is the sum of labels assigned to edges incident to the vertex u. In this paper, we prove that the splittance of an anti-magic graph admits anti-magic labeling. It was conjectured by Hartsfield and Ringel that every tree other than K₂ has an anti-magic labeling. In this paper, we prove that there exists infinitely many trees that are anti-magic.

How to Cite

S. Muthukkumar, K. Rajendran, Generation of Anti-Magic Graphs, Int. J. Anal. Appl. 23 (2025), 30. https://doi.org/10.28924/2291-8639-23-2025-30

BibTeX

@article{Muthukkumar2025,
  author  = {Muthukkumar, S. and Rajendran, K.},
  title   = {Generation of Anti-Magic Graphs},
  journal = {Int. J. Anal. Appl.},
  volume  = {23},
  year    = {2025},
  pages   = {30},
  doi     = {10.28924/2291-8639-23-2025-30}
}

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