The Middle Equitable Dominating Graphs


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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] K. D. Dharmalingam, “Studies in Graph Theorey-Equitable Domination and Bottleneck Domination,” Ph.D. Thesis, Madurai Kamaraj University, Madurai, 2006.
[2] F. Harary, “Graph Theory,” Addison-Wesley, Boston, 1969.
[3] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, “Fundamentals of Domination in Graphs,” Marcel Dekker, Inc., New York, 1998.
[4] V. R. Kulli and B. Janakiram, “The Minimal Dominating Graph,” Graph Theory Notes of New York, Vol. 28, Academy of Sciences, New York, 1995, pp. 12-15.
[5] V. R. Kulli, B. Janakiram and K. M. Niranjan, “The Common Minimal Domi-nating Graph,” Indian Journal of Pure and Applied Mathematics, Vol. 27, No. 2, 1996, pp. 193196.
[6] V. R. Kulli, B. Janaki-ram and K. M. Niranjan, “The Vertex Minimal Dominating Graph,” Acta Ciencia Indica, Vol. 28, 2002, pp. 435-440.
[7] V. R. Kulli, B. Janakiram and K. M. Niranjan, “The Dominating Graph,” Graph Theory Notes of New York, Vol. 46, New York Academy of Sciences, New York, 2004, pp. 5-8.
[8] H. B. Walikar, B. D. Acharya and E. Sampathkumar, “Recent Developments in the Theory of Domination in Graphs,” MRI Lecture Notes in Mathematices, Vol. 1, Mehta Research Institute, Alahabad, 1979.

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