Equitable Power Domination Number of Certain Graphs

  • Authors

    • S. Banu Priya
    • N. Srinivasan
    2018-10-02
    https://doi.org/10.14419/ijet.v7i4.10.20933
  • Dominating set, Equitable dominating set, Power dominating set, Equitable power dominating set, Equitable power domination number.
  • Let   12G">  be a graph with vertex set 12V"> , a set 12Sâٹ†V">  is said to be a power dominating set (PDS), if every vertex  12u∈V-S">  is observed by some vertices in 12S">  using the following rules: (i) if a vertex  12v">  in 12G">  is in PDS, then it dominates itself and all the adjacent vertices of 12v">  and (ii) if an observed vertex 12v">  in 12G">  has  12k>1">  adjacent vertices and if 12k-1">  of these vertices are already observed, then the remaining one non-observed vertex will also be observed by 12v">  in 12G"> . The degree 12d(v)">  of a vertex 12v">  in 12G">  is the number of edges of 12G">  incident with 12v">  and any two adjacent vertices 12u">  and 12v">  in 12G">  are said to hold equitable property if 12|d(u)-d(v)| ≤ 1"> . In this paper, we introduce the notions of equitable power dominating set and equitable power domination number. We also derive the equitable power domination number of certain graphs.

     

     

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  • How to Cite

    Banu Priya, S., & Srinivasan, N. (2018). Equitable Power Domination Number of Certain Graphs. International Journal of Engineering & Technology, 7(4.10), 349-354. https://doi.org/10.14419/ijet.v7i4.10.20933