Equitable Power Domination Number of Mycielskian of Certain Graphs

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 between the degree of and degree of is less than or equal to 1, i.e., . The minimum cardinality of an equitable power 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.