Show that the following statements are equivalent.
- $G$ is connected and has $n-1$ edges.
- $G$ is a forest and has $n-1$ edges.
- $G$ is a tree.
A $Graph$ is said to be connected if every pair of distinct vertices is joined by a path.
A $Tree$ is an undirected, connected graph containing no cycles.
A $Forest$ graph is an undirected graph in which any two vertices are connected by at most one path. Equivalently a forest is an undirected acyclic graph.
Our graph $G$ here is a simple graph with $n$ vertices.
I am confused where to start. Please help me show these.