Edge B-E is skipped because both of its endpoints (B and E) are already in the visited set (MST). Prim's algorithm only considers edges that connect a visited vertex to an unvisited vertex to avoid creating cycles.
Conditions: Both endpoints of the edge are already marked as visited.; The algorithm strictly follows the rule of adding only crossing edges.
Edge B-E is skipped because both of its endpoints (B and E) are already in the visited set (MST). Prim's algorithm only considers edges that connect a visited vertex to an unvisited vertex to avoid creating cycles.
Conditions: Both endpoints of the edge are already marked as visited.; The algorithm strictly follows the rule of adding only crossing edges.
Edge A-B is chosen first because Prim's algorithm is a greedy algorithm that selects the smallest edge connecting the current visited set to an unvisited node. From the starting node A, edge A-B has the minimum weight among all edges incident to A leading to unvisited nodes.
Conditions: Node A is the starting visited node.; The algorithm follows the greedy rule of picking the minimum-weight crossing edge.
Edge A-B is chosen first because Prim's algorithm is a greedy algorithm that selects the smallest edge connecting the current visited set to an unvisited node. From the starting node A, edge A-B has the minimum weight among all edges incident to A leading to unvisited nodes.
Conditions: Node A is the starting visited node.; The algorithm follows the greedy rule of picking the minimum-weight crossing edge.