Maximum graphs with unique minimum dominating set of size two.
Michael Fraboni, Nathan Shank · Australas. J Comb. · 2010
We prove that the maximum number of edges of a graph of order n which has a unique minimum dominating set of size two is bounded above by ( n−2 2 ) . As a corollary to this result, we prove a conjecture by Fischermann, Rautenbach and Volkmann that the maximum number of edges of a graph which has a unique minimum dominating set of size two is ( n−2 2 ) .