Quoting from Dasgupta, Papadimitrou, and Vazirani textbook:
“Trees A tree is an undirected graph that is connected and acyclic.”p.135
Trees have these properties, quoting from DPV again:
- A tree on n nodes has n − 1 edges
- Any connected, undirected graph G = (V, E) with |E| = |V| − 1 is a tree.
- An undirected graph is a tree if and only if there is a unique path between any pair of nodes.