• A. Parthiban
• S. Banu Priya

Let G (V, E) be graph. A set S ⊆ V is said to be a power dominating set (PDS) if every vertex u ∈ V-S is observed by certain vertices in S by the following rules: (i) if a vertex v in G is in PDS, then it dominates itself and all the adjacent vertices of v and (ii) if an observed vertex v in G has k > 1 adjacent vertices and if k-1 of these vertices are already observed, then the remaining one non-observed vertex is also observed by v in G. A power dominating set S ⊆ V in G (V,E) is said to be an equitable power dominating set (EPDS), if for every vertex v ∈ V-S there exists an adjacent vertex u ∈ S such that the difference between the degree of u and degree of v is less than or equal to 1, i.e., |d(u)-d(v)|≤ 1. The minimum cardinality of an equitable power dominating set of G is called the equitable power domination number of G, denoted by γ_epd (G). “An edge is said to be subdivided if the edge xy is replaced by the path: xwy, where w is the new vertex. A graph obtained by subdividing each edge of a graph G is called subdivision of G, and is denoted by S(G)". In this paper we establish the equitable power domination number of subdivision of certain classes of graphs. We also obtain the equitable power domination number of the generalized Petersen graphs and balanced binary tree.

Power dominating set, Power domination number, Equitable power dominating set, Equitable power domination number, Generalized Petersen graphs, Balanced binary tree, and Subdivision graph.

"Equitable Power Domination Number of Generalized Petersen Graph, Balanced Binary Tree and Subdivision of Certain Graphs", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 1, page no.730-737, January 2019, Available :http://www.jetir.org/papers/JETIRDY06117.pdf

"Equitable Power Domination Number of Generalized Petersen Graph, Balanced Binary Tree and Subdivision of Certain Graphs", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 1, page no. pp730-737, January 2019, Available at : http://www.jetir.org/papers/JETIRDY06117.pdf