Equitable Power Domination Number of Certain Graphs - Banu Priya, S.; Srinivasan, N. (International Journal of Engineering and Technology, 2018)
Let Â 12G"> Â be a graph with vertex set 12V"> , a set 12SÃ¢Ù¹â€ V"> Â is said to be a power dominating set (PDS), if every vertexÂ 12uÃ¢Ë†Ë†V-S"> Â is observed by some vertices in 12S"> Â using the following rules: (i) if a vertexÂ 12v"> Â in 12G"> Â is in PDS, then it dominates itself and all the adjacent vertices of 12v"> Â and (ii) if an observed vertex 12v"> Â in 12G"> Â hasÂ 12k>1"> Â adjacent vertices and if 12k-1"> Â of these vertices are already observed, then the remaining one non-observed vertex will also be observed by 12v"> Â in 12G"> . The degree 12d(v)"> Â of a vertex 12v"> Â in 12G"> Â is the number of edges of 12G"> Â incident with 12v"> Â and any two adjacent vertices 12u"> Â and 12v"> Â in 12G"> Â are said to hold equitable property if 12|d(u)-d(v)| Ã¢â€°Â¤ 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.Â Â