graph theory: Prove by induction that the eccentricity of

[mooshupork34]

I have to prove by induction that the eccentricity of a vertex in a a tree T' (one that has all its leaves, vertices of degree 1, removed) is 1 less than the eccentricity of that vertex in T (the tree that still has its leaves).

So far I have a base case which is that if you have two points connected by an edge, then removing one leaf would give that remaining point an eccentricity of 0.

I'm not sure how to go about the rest, though, so if anyone could show me - I would appreciate it!

 

[daon]

I'd attempt to help you if the question can be made more clear to me. What is the parameter that you are inducting on? Try writing the full question with every little comment there might be.

Also, your base case doesn't make sense to me, as if you have two nodes connected through a single edge, removing all nodes of degree one would leave no vertecies left.

-Daon