On 3-γt-vertex critical graphs of diameter three

A total dominating set of a graph G=(V,E) with no isolated vertex is a set S⊆V such that every vertex is adjacent to a vertex in S. The minimum cardinality of a total dominating set of G is the total domination number γt(G) of G. Let k≥3 be an integer. A graph G with no isolated vertex is k-γt-vertex critical if γt(G)=k and γt(G−v)