OJDM  Vol.2 No.3 , July 2012
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 Med(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 Kp∈Med(G) . Other properties of middle equitable dominating graphs are also obtained.
Cite this paper: A. Alwardi, N. Soner and A. Al-Kenani, "The Middle Equitable Dominating Graphs," Open Journal of Discrete Mathematics, Vol. 2 No. 3, 2012, pp. 93-95. doi: 10.4236/ojdm.2012.23017.

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