Total domination excellent trees (Q1869221)

A set \(S\) of vertices of a graph \(G\) is a total dominating set if every vertex of \(G\) is adjacent to some vertex of \(S\) (other than itself). A graph is total domination excellent, denoted by \(\gamma_t\)-excellent, if every vertex belongs to some total dominating set of smallest cardinality. The author shows that the class of \(\gamma_t\)-excellent trees can be constructed recursively by starting with a star and repeatedly applying one of four operations.