To ensure mutual reachability between every pair of vertices, the directed graph must contain at least one directed cycle that covers all n vertices. A directed cycle with n vertices has exactly n edges, which is the minimum required for strong connectivity.
Conditions: G is a directed graph.; G has n vertices.; G is a strongly connected graph.
To ensure mutual reachability between every pair of vertices, the directed graph must contain at least one directed cycle that covers all n vertices. A directed cycle with n vertices has exactly n edges, which is the minimum required for strong connectivity.
Conditions: G is a directed graph.; G has n vertices.; G is a strongly connected graph.
Connectivity in an undirected graph only requires the existence of a path between two vertices, not a direct edge. Vertices can be connected consecutively through a sequence of intermediate edges.
Conditions: Applies to undirected graphs.; Connectivity is judged by the existence of a path, not direct adjacency.
Connectivity in an undirected graph only requires the existence of a path between two vertices, not a direct edge. Vertices can be connected consecutively through a sequence of intermediate edges.
Conditions: Applies to undirected graphs.; Connectivity is judged by the existence of a path, not direct adjacency.