To ensure that any two vertices are reachable from each other, the graph must have at least n-1 edges. This minimum is achieved when the graph forms a tree-like structure, such as a star graph, where edges connect vertices without forming cycles.
Conditions: G is an undirected graph.; G has n vertices.; G is a connected graph.
To ensure that any two vertices are reachable from each other, the graph must have at least n-1 edges. This minimum is achieved when the graph forms a tree-like structure, such as a star graph, where edges connect vertices without forming cycles.
Conditions: G is an undirected graph.; G has n vertices.; G is a 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.