Proof: A Bridge is the Unique Path connecting its End Vertices | Graph Theory

If e=uv is a bridge of a graph, then there exists a unique path connecting u and v, and this path is the bridge itself! We'll be proving this result about bridges and their end vertices in today's graph theory lesson!
Recall that a bridge of a connected graph is an edge that when deleted disconnects the graph. We can also say that a bridge of a disconnected graph is an edge that, when deleted, disconnects the component it belongs to. The result we prove today tells us that not only is a graph disconnected when a bridge is removed, but in particular - the end vertices of the bridge become disconnected.
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[@aroobashahoor599]

Underrated video, this was one of the hardest proofs I had encountered which was not explained well in the book I have :) Thanks!!

[@PunmasterSTP]

Thanks for showing us the path forward 😎

[@jephtekayabo8655]

Consider a tree T with n vertices, where n is an odd integer greater than or equal to 3. Let v be a vertex of T. Prove that there exists a vertex u in T such that the distance between u and v is at most (n-1)/2.