Total domination in maximal outerplanar graphs

We show that the total domination number of a maximal outerplanar graph G is bounded above by n+k3, where n is the order of G and k is the number of vertices of degree 2. For k>n3, a better bound is given by 2(n−k)3. For k>n3, we improve the upper bound of n+k4 on the usual domination number.