The Eccentric Empire
In Sheldor's empire, the cities form a tree with cities as vertices and roads as edges. He wishes to choose a capital among his cities and to do that, his ministers come up with the following definition:
- The eccentricity of a city \(v\) is the maximum distance from \(v\) to any vertex.
Sheldor wishes to choose a city which is the least eccentric. What is the maximum number of such cities that could exist?