## Connected graphs with maximum total domination number.(English)Zbl 0958.05100

For any ordinary graph $$G=(V,E)$$, the total domination number $$\gamma_t(G)$$ is the minimum cardinality of subsets $$S$$ of $$V$$ such that every vertex of $$V$$ has a neighbour in $$S$$. It is known [E. J. Cockayne, R. M. Dawes and S. T. Hedetniemi, Total domination in graphs, Networks 10, 211-219 (1980; Zbl 0447.05039)] that $$\gamma_t\geq\lfloor\frac{2n}3\rfloor$$, for $$|V|>2$$. This paper characterizes graphs that attain that bound.

### MSC:

 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C75 Structural characterization of families of graphs 05C35 Extremal problems in graph theory

Zbl 0447.05039