10.1186/2251-7456-6-45

The edge-labeling and vertex-colors of Kn

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  • Mohammad hadi Alaeiyan*1,
  1. Department of Computer Enginering, Iran University of Science and Technology, Tehran, Narmak, 16844, IR
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Published in Issue 2012-10-04

How to Cite

Alaeiyan, M. hadi. (2012). The edge-labeling and vertex-colors of Kn. Mathematical Sciences, 6(1). https://doi.org/10.1186/2251-7456-6-45
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Abstract

Abstract A labeling of the edges of a graph is called vertex-coloring if the labeled degrees of the vertices yield a proper coloring of the graph. In this paper, we show that such a labeling is possible from the label set 1,2,3 for the complete graph K n , n ≥ 3.

Keywords

  • Edge-labeling,
  • Vertex-coloring,
  • Complete graph,
  • 05C15,
  • 05C78
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References

  1. Kalkowski M, Kalkowski: A note on the 1,2-conjecture. submitted for publication.
  2. Karonskiy et al. (2004) Edge weights and vertex colours (pp. 151-157) https://doi.org/10.1016/j.jctb.2003.12.001
  3. Addario-Berry et al. (2007) Vertex-colouring edge-wheitings (pp. 1-12) https://doi.org/10.1007/s00493-007-0041-6
  4. Addario-Berry et al. (2008) Degree constrained subgraphs (pp. 1168-1174) https://doi.org/10.1016/j.dam.2007.05.059
  5. Wang and Yu (2008) On vertex-coloring 13-edge-weighting (pp. 1-7) https://doi.org/10.1007/s11461-008-0009-8
  6. Kalkowski et al. (2003) Vertax-Coloring Edge-Weithings With Integer Weights At Most 6 (pp. 101-119)
  7. Kalkowski et al. (2010) Vertex-coloring edge-weightings: Towardsthe1-2-3-conjecture (pp. 347-349) https://doi.org/10.1016/j.jctb.2009.06.002