Author(s)

Anwar Alwardi, N.D. Soner, Ahmad N. Al-Kenani

Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
Department of Studies in Mathematics, University of Mysore, Mysore 570 006, India.

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.

Eqitable Domination Number; Middle Equitable Dominating Graph; Intersection Graphs

Alwardi, A. , Soner, N. and Al-Kenani, A. (2012) The Middle Equitable Dominating Graphs. Open Journal of Discrete Mathematics, 2, 93-95. doi: 10.4236/ojdm.2012.23017.