The Middle Equitable Dominating Graphs

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.

DOI: 10.4236/ojdm.2012.23017                

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.

Keywords

Eqitable Domination Number; Middle Equitable Dominating Graph; Intersection Graphs

Conflicts of Interest

The authors declare no conflicts of interest.

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