A graph G is domination bicritical if the removal of any pair of vertices decreases the domination number. Properties of bicritical graphs are studied. We show that a connected bicritical graph has domination number at least 3, minimum degree at least 3, and edge-connectivity at least 2. Ways of constructing a bicritical graph from smaller bicritical graphs are presented.
Brigham, Robert C.; Haynes, Teresa W.; Henning, Michael A.; and Rall, Douglas F.. 2005. Bicritical Domination. Discrete Mathematics. Vol.305(1-3). 18-32. https://doi.org/10.1016/j.disc.2005.09.013 ISSN: 0012-365X