The Middle Equitable Dominating Graphs

Abstract

Let G = ( V, E ) be a graph and A(G) is the collection of all minimal equitable dominating set of G . The middle equitable dominating graph of G is the graph denoted by M ed ( G ) with vertex set the disjoint union of V∪A(G) and ( u, v ) is an edge if and only if u ∩ v ≠ φ whenever u, v ∈ A(G) or u ∈ v whenever u ∈ v and v ∈ A(G) . In this paper, characterizations are given for graphs whose middle equitable dominating graph is connected and K p ∈M ed (G) . Other properties of middle equitable dominating graphs are also obtained.