Total domination edge critical graphs

Abstract

Denote the total domination number of a graph G by _γt(G). A graph G is said to be total domination edge critical, or simply _γt-critical, if _γt(G + e) < _γt(G) for each edge e ∈ E(Ḡ). In this introductory paper we give some basic results on _γt-critical graphs, discuss properties of 3_t-critical graphs, that is, _γt-critical graphs with _γt = 3, and characterise the 3_t-critical graphs which contain cutvertices.