We show that the total domination number of a maximal outerplanar graph G is bounded
above by n+ k 3, where n is the order of G and k is the number of vertices of degree 2. For k>
n 3, a better bound is given by 2 (n− k) 3. For k> n 3, we improve the upper bound of n+ k 4
on the usual domination number.

The total domination number of a graph is the minimum size of a set S such that every vertex
has a neighbor in S. We show that a maximal outerplanar graph of order n≥ 5 has total
domination number at most 2 n/5, apart from two exceptions, and this bound is best possible.