The Middle Dominating Graph of a Graph
Bommanahal Basavanagoud, Sunilkumar M. Hosamani · 2010
Let G = (V,E) be a graph and A(G) is the collection of all minimal dominating set of G. The middle dominating graph of G is the graph denoted by Md(G) with vertex set the disjoint union of V [ A(G) and (u,v) is an edge if and only if u v 6 whenever u,v 2 A(G) or u 2 v whenever u 2 V and v 2 A(G). In this paper, characterizations are given for graphs whose middle dominating graph is connected and Kp Md(G). Other properties of middle dominating graphs are also obtained.