Prime Graceful Labeling

  • Authors

    • T. Hameed Hassan
    • R. Mohammad Abbas
    2018-12-09
    https://doi.org/10.14419/ijet.v7i4.36.24234
  • Prime labeling, graceful labeling and prime graceful labeling.

  • Abstract

    A graph G with m vertices and n edges, is said to be prime graceful labeling, if there is an injection   from the vertices of G to {1, 2, ..., k} where k = min {2m, 2n} such that  gcd ( ( ),  ( )=1 and the induced injective function   from the edges of G to {1, 2, ..., k − 1} defined by  ( ) = |  ( ) − ( ) | , the resulting edge labels are distinct. In this paper path  , cycle Cn , star K1,n , friendship graph Fn , bistar Bn,n, C4 ∪ Pn , Km,2 and Km,2 ∪ Pn are shown to be Prime Graceful Labeling .

     

  • References

    1. [1] Tout R, Dabboucy AN & Howalla K, “Prime labeling of graphsâ€, National Academy Science Letters-India, Vol.5, No.11, (1982), pp.365-368.

      [2] Harary F, Graph Theory, Addison-Wesley, Reading, Mass, (1969).

      [3] Bondy JA & Murthy USR, “Graph theory with applicationsâ€, Elsevier North Holland. New York, (1976).

      [4] Gallian JA, “A dynamic survey of graph labelingâ€, The electronic journal of combinatory, Vol.16, No.6, (2009), pp.1-219.

      [5] Rosa A, “On certain valuations of the vertices of a graphâ€, Theory of Graphs (Internet Symposium, Rome, (1966), pp.349-355.

      [6] Uma R & Murugesan, N, “Graceful labeling of some graphs and their sub graphsâ€, Asian Journal of Current Engineering and Maths, Vol.1, No.6, (2013), pp.307-370.

      [7] Vaidya SK & Vihol PL, “Prime cordial labeling for some cycle related graphsâ€, International Journal of Open Problems in Computer Science and Mathematics, Vol.3, No.5, (2010), pp.98-104.

      [8] Vaidya SK & Shah NH, “Graceful and odd graceful labeling of some graphsâ€, International journal of Mathematics and soft computing, Vol.3, No.1, (2013), pp.61-68.

      [9] Singhun S, “Graphs with line-odd Graceful labelingâ€, International Mathematics Forum, Vol.8, No.12, (2010), pp.577-582.

      [10] Sridevi R, Navaneethakrishnan S & Nagarajan K, “Super Fibonacci graceful labeling of some special class of graphsâ€, Mathematical Combinatory, Vol.1, (2011), pp.59-72.

  • Downloads

  • How to Cite

    Hameed Hassan, T., & Mohammad Abbas, R. (2018). Prime Graceful Labeling. International Journal of Engineering & Technology, 7(4.36), 750-752. https://doi.org/10.14419/ijet.v7i4.36.24234

    Received date: 2018-12-18

    Accepted date: 2018-12-18

    Published date: 2018-12-09