Effective Conversion of Non-Prime Graphs to Prime Graphs
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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
- J.A. Bondy, U.S.R. Murty, Graph Theory With Applications, Macmillan, London, (1976).
- H. Fu, K. Huang, On Prime Labellings, Discret. Math. 127 (1994), 181–186. https://doi.org/10.1016/0012-365x(92)00477-9.
- J.A. Gallian, A Dynamic Survey of Graph Labeling, Electron J. Comb. 2023 (2023), #DS6. https://doi.org/10.37236/27.
- A.D. Tout, A.N. Dabboucy, K. Howalla, Prime Labeling of Graphs, Nat. Acad. Sci. Lett. 11 (1982), 365–368.
- M.A. Seoud, M.Z. Youssef, On Prime Labeling of Graphs, Congr. Numer. 141 (1999) 203–215.
- 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.
- 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.
- R. Frucht, F. Harary, On the Corona of Two Graphs, Aequ. Math. 4 (1970), 322–325. https://doi.org/10.1007/bf01844162.
- 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).
- S.M. Lee, I. Wui, J. Yeh, On the Amalgamation of Prime Graphs, Bull. Malays. Math. Soc. 11 (1988), 59–67.
- 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.