2. (25 points) Given a connected acyclic graph (a free tree) T and a node v of T, the eccentricity of v is the length of a longest path from v to any other node of T. A node of T with minimum eccentricity is called a center of T. (a) Design an O(EI) time algorithm that computes a center of T. (b) Is the center unique? If yes, prove it. If not, give an example to show there could be more than one center of T