Proof: Graph with n Vertices and n-1 Edges is a Tree | Graph Theory

A connected graph with n vertices and n-1 edges must be a tree! We'll be proving this result in today's graph theory lesson! We previously proved that a tree graph with n vertices must have n-1 edges, so this gives us a characterization of tree graphs as follows.

A connected graph is a tree if and only if it has one less edge than vertices.

Proof that trees have one less edge than vertices:    • Proof: Tree Graph of Order n Has Size...  

Proof that edges are bridges iff they lie on a cycle:    • Proof: An Edge is a Bridge iff it Lie...  

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