A graph 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-dot-critical graph G with G' = aleph is 2-connected? In this note, we give a family of 1-connected 2k-dot-critical graph with G' = aleph and show that this problem has a negative answer.
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