Equitable Power Domination Number of Mycielskian of Certain Graphs - Banu Priya, S.; Parthiban, A.; Srinivasan, N. (International Journal of Engineering and Technology, 2018)
Let Â be a simple graph with vertex set Â and edge set . A set Â is called a power dominating set (PDS), if every vertexÂ Â is observed by some vertices in Â by using the following rules: (i) if a vertex Â in Â is in PDS, then it dominates itself and all the adjacent vertices of Â and (ii) if an observed vertex Â in Â has Â adjacent vertices and ifÂ Â of these vertices are already observed, then the remaining one non-observed vertex is also observed by Â in . A power dominating set Â Â inÂ Â is said to be an equitable power dominating set (EPDS), if for every Â there exists an adjacent vertexÂ Â such that the difference between the degree of Â and degree of Â is less than or equal to 1, i.e., . The minimum cardinality of an equitable power dominating set of Â is called the equitable power domination number of Â and denoted by . The Mycielskian of a graph Â is the graph Â with vertex set Â where , and edge set Â In this paper we investigate the equitable power domination number of Mycielskian of certain graphs.Â