Global domination edge critical graphs - Desormeaux, Wyatt J.; Haynes, Teresa W.; Van Der Merwe, Lucas (Utilitas Mathematica, 2017)
A set S of vertices in a graph G is a global dominating set of G if 5 simultaneously dominates both G and its complement G. The minimum cardinality of a global dominating set of G is the global domination number of G. We study the graphs for which removing any arbitrary edge from G and adding it to G decreases the global domination number.