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.
Unlike an undirected graph, a directed graph allows two oppositely directed edges between the same pair of distinct vertices. Therefore, the maximum number of edges is exactly twice the maximum number of edges in an undirected complete graph, yielding n(n−1).
Conditions: G is a directed graph.; G has n vertices.; We are seeking the maximum possible number of edges.
Unlike an undirected graph, a directed graph allows two oppositely directed edges between the same pair of distinct vertices. Therefore, the maximum number of edges is exactly twice the maximum number of edges in an undirected complete graph, yielding n(n−1).
Conditions: G is a directed graph.; G has n vertices.; We are seeking the maximum possible number of edges.