The Middle Equitable Dominating Graphs

DOI: 10.4236/ojdm.2012.23017   PDF   HTML   XML   3,429 Downloads   7,358 Views  

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.

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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.

References

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