Copyright © 2018 Authors. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestrict- ed use, distribution, and reproduction in any medium, provided the original work is properly cited. International Journal of Engineering & Technology, 7 (4.10) (2018) 842-845 International Journal of Engineering & Technology Website: www.sciencepubco.com/index.php/IJET Research paper Equitable Power Domination Number of Mycielskian of Certain Graphs S. Banu Priya 1 *, A. Parthiban 2 , N. Srinivasan 1 1 Department of Mathematics, St. Peter's Institute of Higher Education and Research Avadi, Chennai - 600 054, Tamil Nadu, India 2 Department of Mathematics, School of Chemical Engineering and Physical Sciences Lovely Professional University, Phagwara - 144 411, Punjab, India *Corresponding author E-mail: banupriyasadagopan@gmail.com Abstract Let   be a simple graph with vertex set  and edge set . A set  is called a power dominating set (PDS), if every vertex    is observed by some vertices in  by using the following rules: (i) if a vertex  in  is in PDS, then it dominates itself and all the adjacent vertices of  and (ii) if an observed vertex  in  has    adjacent vertices and if  of these vertices are already observed, then the remaining one non-observed vertex is also observed by  in . A power dominating set  in   is said to be an equitable power dominating set (EPDS), if for every  there exists an adjacent vertex   such that the difference be- tween the degree of  and degree of  is less than or equal to 1, i.e.,     . The minimum cardinality of an equitable pow- er dominating set of  is called the equitable power domination number of  and denoted by   . The Mycielskian of a graph  is the graph  with vertex set      where       , and edge set            In this paper we investigate the equitable power domination number of Mycielskian of certain graphs. Keywords: Dominating set; Equitable dominating set; Power dominating set; Equitable power dominating set; Equitable power domination number, Mycielskian graph. 1. Introduction All the graphs considered in this paper are finite, connected, sim- ple, and undirected. The notion of domination in graphs was intro- duced by Hedetniemi and Laskar [7] and the concept of equitabil- ity in the graphs was studied by Swaminathan et al. [9]. Haynes et al. introduced the concept of power domination in graphs and power domination number of graphs. A dominating set [6, 7] of a graph     is a set  of vertices such that every vertex  in  has at least one neighbor in . The minimum cardinality of a dominating set of  is called the domination number of  and denoted by   . The degree  of a vertex  in  is the total number of edges of  incident with  and any two adjacent vertices  and  in  are said to hold equita- ble property if     . A dominating set    in     is called equitable dominating set [1] if for every    there exists an adjacent vertex  such that the difference between degree of  and degree of  is less than or equal to 1, that is     . The minimum cardinality of an equitable dominating set of  is said to be equitable domi- nation number of  and denoted by   . A set    is called a power dominating set (PDS) [2, 4] of  if every vertex  is observed by some vertices in  by using the following rules: If a vertex  in  is in PDS, then it dominates itself and all the adjacent vertices of . If an observed vertex  in  has    adjacent vertices and if  of these vertices are already observed, then the remaining one non-observed vertex is also observed by  in  The minimum cardinality of an power dominating set of  is called the power domination number of  and denoted by   . Banu Priya et al. introduced the concept of equitable power domi- nation in graphs [3]. A power dominating set    in    is said to be an equitable power dominating set, if for every vertex  there exists an adjacent vertex    such that the difference between degree of  and degree of  is less than or equal to 1, that is      The minimum cardinality of an equitable power dominating set of  is said to be the equita- ble power domination number of  and denoted by    It is interesting to note that the equitable power dominating set  of a graph  is not unique. Let   be a graph. The Mycielskian of  [10] is the graph  with vertex set      where       , and edge set            We call the vertices of  as the corresponding vertices of  for convenience sake. In this paper we establish the equitable power domination number of Mycielskian of certain graphs. 2. The Equitable Power Domination Number of the Myceilskian of Cycle and Path One can note that the equitable power domination number of the Mycielskian of a cycle   , for      is 2. One such exam- ple is given in Figure. 1.