Effective Conversion of Non-Prime Graphs to Prime Graphs

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Karnam Gurunadhan Tharunraj, P. Ragukumar

Abstract

A graph G is considered to have a prime labeling when each of its n vertices is assigned a unique label from the set {1, 2, 3, 4, ..., n}, ensuring that the labels of any two connected vertices are coprime. In the literature, many graph classes identified as prime graphs and non-prime graphs. In this paper, we focus on converting non-prime graph classes to a prime graph classes by applying corona product with complete graph on one vertex.

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References

  1. J.A. Bondy, U.S.R. Murty, Graph Theory With Applications, Macmillan, London, (1976).
  2. H. Fu, K. Huang, On Prime Labellings, Discret. Math. 127 (1994), 181–186. https://doi.org/10.1016/0012-365x(92)00477-9.
  3. J.A. Gallian, A Dynamic Survey of Graph Labeling, Electron J. Comb. 2023 (2023), #DS6. https://doi.org/10.37236/27.
  4. A.D. Tout, A.N. Dabboucy, K. Howalla, Prime Labeling of Graphs, Nat. Acad. Sci. Lett. 11 (1982), 365–368.
  5. M.A. Seoud, M.Z. Youssef, On Prime Labeling of Graphs, Congr. Numer. 141 (1999) 203–215.
  6. S.K. Vaidya, U.M. Prajapati, Prime Labeling in the Context of Duplication of Graph Elements, Int. J. Math. Soft Comput. 3 (2013), 13–20. https://doi.org/10.26708/ijmsc.2013.1.3.01.
  7. R.K. Guy, F. Harary, On the Möbius Ladders, Can. Math. Bull. 10 (1967), 493–496. https://doi.org/10.4153/cmb-1967-046-4.
  8. R. Frucht, F. Harary, On the Corona of Two Graphs, Aequ. Math. 4 (1970), 322–325. https://doi.org/10.1007/bf01844162.
  9. T. Deretsky, S.M. Lee, J. Mitchem, On Vertex Prime Labelings of Graphs, in: Graph Theory, Combinatorics, and Applications, vol. 1, pp. 359–369, Wiley, New York, (1991).
  10. S.M. Lee, I. Wui, J. Yeh, On the Amalgamation of Prime Graphs, Bull. Malays. Math. Soc. 11 (1988), 59–67.
  11. J. Ashwini, S.P. Selvam, R.B. Gnanajothi, Some New Results on Lucky Labeling, Baghdad Sci. J. 20 (2023), 50. https://doi.org/10.21123/bsj.2023.8569.