Neighborhood Connected Two -Outdegree Equitable Domination of the Ï‘-Obrazom Graphs of P_n,G_n and H_n

  • Authors

    • K. Ameenal Bibi
    • P. Rajakumari
    2018-10-02
    https://doi.org/10.14419/ijet.v7i4.10.21025
  • Connected two-outdegree equitable number, Line graph, Neighborhood connected two-outdegree equitable number, Two-outdegree equitable domination number.
  • Let G=(V,E) be a connected graph. A two-outdegree equitable dominating set D of a graph G is called the neighborhood connected two-outdegree equitable dominating set (nc2oe-set) if the induced sub graph <N(D)> is connected. The minimum cardinality of the minimal neighborhood connected two-outdegree equitable dominating set is called neighborhood connected two-outdegree equitable domination number of G and is denoted by . In this paper, we initiated the a study of this parameter and obtained  for the -obrazom graphs of  and . Also, we investigated the two-outdegree equitable domination number of the -obrazom graphs of  and .

     

     

  • References

    1. [1] Anitha S, Arumugam and Mustapha Chellai (2011), Equitable Domination in Graphs. Discrete Math. Algorithm.Appl. 03, 311.

      [2] Arumugam S. and Sivagnanam C (2010), Neighborhood connected domination in graphs. J. Combin. Math, Combin, Comput., Vol.73, PP.55-64.

      [3] Chartrand G and Lesniak L (2005), Graphs and Digraphs. Chapman and Hall. CRC, 4th edition.

      [4] Haynes TW, Hedetniemi ST and Slater PJ (1998), Fundamentals of Domination in Graphs. Marcel Dekker Inc. New York, U.S.A.

      [5] Haynes TW, Hedetniemi ST and Slater PJ (1998), Domination in Graphs Advanced Topics. Marcel Dekker Inc. New York, U.S.A.

      [6] Mahesh MS and Namsivayam P (2015) Neighborhood Connected two-out degree equitable domination number for some standard graphs. International Journal of Mathematical Archive 6(2) , 156-163.

      [7] Mohammed Alatif , Puttaswamy Rangaiah, Nayaka SR (2016), Boundary domination of line and middle graph of wheel graph families. International journal of computer Applications(0975-8887) volume 134-No.5.

      [8] Sahal A and Mathad V(2013), Two-out degree equitable domination in graphs. Transaction on combinatorics vol 2.No. 3.

      [9] Sampath Kumar E and Walikar HB (1979), The connected domination number of a graph. J.Math. Physics. Sci 13, 607-613.

      [10] Siva Kumar S, Soner ND, Anwar Alwardi and Deepak G (2012), Neighborhood Connected Equitable Domination in Graphs. Applied Mathematical Science Vol 6, No.50, 2445-2452.

      [11] Thilagavathi and Vernold Vivin J (2009), “On Harmonious coloring of line graph of central graph of Paths. Applied Mathematical Sciences Vol 3, 2009, No.5,205-214.

      [12] Vernold Vivin J, Venkatachalam.M (2015), On b-chromatic number of sunlet graph and wheel graph families. Journal of the Egyptian Mathematical society 23, 215-218.

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  • How to Cite

    Ameenal Bibi, K., & Rajakumari, P. (2018). Neighborhood Connected Two -Outdegree Equitable Domination of the Ï‘-Obrazom Graphs of P_n,G_n and H_n. International Journal of Engineering & Technology, 7(4.10), 399-402. https://doi.org/10.14419/ijet.v7i4.10.21025