I stuck in one challenging question, I read on my notes.
An undirected, weighted, connected graph $G$, (with no negative weights and with all weights distinct) is given. We know that, in this graph, the shortest path between any two vertices is on the minimum spanning tree (MST). Verify the following:
1) shortest path between any two vertices $u$, $v$ is unique.
My question is, is this statement (1) is false or True?
Other details is not mentioned in the old exam question, But I think:
if we consider Any shortest path must be on MST The statement is True, if consider there exists a shortest path on MST this is false.