TITLE:
The Middle Equitable Dominating Graphs
AUTHORS:
Anwar Alwardi, N.D. Soner, Ahmad N. Al-Kenani
KEYWORDS:
Eqitable Domination Number; Middle Equitable Dominating Graph; Intersection Graphs
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.2 No.3,
July
18,
2012
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.