Tree

Tree: a graph are connected and acyclic

• Trees $⟺$ minimally connected graph aka remove any edge will cause disconnect
• Trees $⟺$ maximally acyclic graph aka add any edge will cause cycle
• $\forall u,v\in V,u\ne v⟹$ unique path from $u$ to $v$
• Free tree is used for an undirected connected acyclic graph without a specific vertex designated as the root.
• Rooted tree with one vertex is designated as the root.

A forest is a collection of (0+) disjoint trees

• A tree is also a forest.
• Total vertices - Total Edges = # trees

Binary Tree: a tree that every vertex has at most two edges incident to it.