  We consider the problem of computing 2-center in maximal outerplanar graph.
In this problem, we want to find an optimal solution where two centers cover
all the vertices with the smallest radius. We provide the following result. We
can compute the optimal centers and the optimal radius in $O(n^2)$ time for a
given maximal outerplanar graph with $n$ vertices. We try to let the maximal
outerplanar graph be cut into two subgraphs with an internal edge, each center
will cover vertices which are continuous.
