AbstractA dominating set in a graph G is a set of vertices D such that every vertex of G is either in D or is adjacent some vertex of D. The domination number Γ(G) of G is the minimum cardinality of any dominating set. A graph is vertex domination‐critical if the removal of any vertex decreases its domination number. This paper gives examples and properties of vertex domination‐critical graphs, presents a method of constructing them, and poses some open questions. In the process several results for arbitrary graphs are presented.