1.- A tree is central if its center is K1 and bicentral if its center is K2. Show that every tree is central or bicentral. ( Kn is call complete graph and it if every two of its vertices are adjacent and every vertex has degree n)
2.- Prove taht a tree with Delta(T)=k ( Delta means maximum degree) has at least k vertices of degree 1.
3.- Prove that in a connected graph G every two longest paths have a common vertex.
Thank you so much for your help.
This solution is comprised of a detailed explanation to show that every tree is central or bicentral.