Total domination edge critical graph

Total domination edge critical graph --- реберно-критический граф тотального доминирования.

A graph [math]\displaystyle{ G }[/math] is defined to be total domination edge critical, or simply [math]\displaystyle{ k_{t} }[/math]-critical, if

[math]\displaystyle{ \gamma_{t}(G + e) \lt \gamma_{t}(G) = k }[/math]

for any edge [math]\displaystyle{ e \in E(\bar{G}) }[/math].

A graph [math]\displaystyle{ G }[/math] is supercritical, if [math]\displaystyle{ \gamma_{t}(G + e) = \gamma_{t}(G) - 2 }[/math] for any [math]\displaystyle{ e \in E(\bar{G}) }[/math], where [math]\displaystyle{ E(\bar{G}) \neq emptyset }[/math].