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An undirected connected graph with n vertices has at least n-1 edges. This minimum is achieved when the graph forms a tree structure.

Conditions: The graph is undirected.; The graph is connected.; The graph has n vertices.

An undirected connected graph with n vertices has at least n-1 edges. This minimum is achieved when the graph forms a tree structure.

Conditions: The graph is undirected.; The graph is connected.; The graph has n vertices.

A strongly connected directed graph with n vertices has at least n edges. This minimum is achieved when the graph forms a single directed cycle.

Conditions: The graph is directed.; The graph is strongly connected.; The graph has n vertices.

A strongly connected directed graph with n vertices has at least n edges. This minimum is achieved when the graph forms a single directed cycle.

Conditions: The graph is directed.; The graph is strongly connected.; The graph has n vertices.

The maximum number of edges in an undirected disconnected graph with n vertices is (n-1)(n-2)/2. This is achieved by forming a complete graph with n-1 vertices and leaving one vertex isolated.

Conditions: The graph is undirected.; The graph is disconnected.; The graph has n vertices.

The maximum number of edges in an undirected disconnected graph with n vertices is (n-1)(n-2)/2. This is achieved by forming a complete graph with n-1 vertices and leaving one vertex isolated.

Conditions: The graph is undirected.; The graph is disconnected.; The graph has n vertices.

A strongly connected graph is a directed graph in which every pair of vertices is mutually reachable. This means that for any two vertices u and v, there is a directed path from u to v and a directed path from v to u.

Conditions: The graph is directed.; The criterion requires mutual reachability between every pair of vertices.

A strongly connected graph is a directed graph in which every pair of vertices is mutually reachable. This means that for any two vertices u and v, there is a directed path from u to v and a directed path from v to u.

Conditions: The graph is directed.; The criterion requires mutual reachability between every pair of vertices.