# Show that every tree is central or bicentral.

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.

© BrainMass Inc. brainmass.com October 9, 2019, 6:43 pm ad1c9bdddfhttps://brainmass.com/math/linear-algebra/show-that-every-tree-is-central-or-bicentral-95949

#### Solution Summary

This solution is comprised of a detailed explanation to show that every tree is central or bicentral.

$2.19