Properties of Trees: Nodes, Paths, and Cycles

This lecture covers the properties of trees in graph theory, including the lemma that a tree with at least one arc has at least two leafs, the relationship between the number of nodes and arcs, the existence of a single path between any two nodes, the formation of cycles by adding arcs, disconnection by removing arcs, and the characterization of a tree in a directed graph. The instructor emphasizes the equivalence of various statements regarding the properties of trees.