# Tree with radius and diameter

How to show that a radius in a tree is not necessarily half its diameter ??

I'm using the following relation to prove but cannot find proper explanation

2*radius-1 ≤ diameter ≤ 2*radius

Suggest if there is any other method.

## 2 Answers

HINT: Every path graph is a tree.

Consider a tree with only $2$ vertices. Then the minimum eccentricity of a vertex (the maximum distance from that vertex to any other), the radius, is $1$. The maximum distance between two vertices, the diameter, is also $1$.