A note on the domination dot-critical graphs ?
A graph G G is dot-critical if contracting any edge decreases the domination number. Nader Jafari Rad (2009)[3] posed the problem: Is it true that a connected k k -dot-critical graph G G with G?=0? G ? = 0? is 2-connected? ? In this note, we give a family of 1-connected 2k 2 k -dot-critical graph with G?=0? G ? = 0? and show that this problem has a negative answer.
domination dot-critical domination number complete bipartite graph