In an undirected graph with 5 vertices, what is the maximum number of edges possible?
10
5
20
25
In the context of Breadth-First Search (BFS), what does it mean for a node to be at 'level i' from the starting node?
The node has 'i' neighbors in the graph.
The node has a priority value of 'i' in the BFS traversal order.
The node is at a distance of 'i' edges away from the starting node.
The node is the i-th node discovered by the BFS algorithm.
In a connected graph, a path that visits every edge exactly once is known as:
Shortest Path
Eulerian Path
Critical Path
Hamiltonian Path
Consider a graph where you want to find if a path exists between two given nodes. Which traversal algorithm would be generally more efficient for this task?
Breadth-First Search (BFS)
Neither DFS nor BFS can determine if a path exists between two nodes.
Depth-First Search (DFS)
Both DFS and BFS have the same efficiency for this task.
Adding an edge between two vertices in an undirected graph always:
Decreases the number of connected components.
May increase or decrease the number of connected components.
Creates a cycle.
Increases the number of connected components.
How does the iterative implementation of Depth-First Search (DFS) typically differ from its recursive counterpart?
The iterative and recursive approaches produce fundamentally different traversal orders.
The iterative approach is generally less efficient in terms of space complexity than recursion.
The iterative approach is not suitable for traversing graphs with cycles.
The iterative approach uses a stack to mimic the function call stack used in recursion.
In an undirected graph, if the sum of the degrees of all vertices is 30, how many edges are there in the graph?
Cannot be determined.
30
15
60
You remove an edge from a connected graph. What is a possible consequence of this action?
The number of cycles in the graph will always decrease.
The graph will always become disconnected.
The number of edges and vertices in the graph will decrease.
The graph may become disconnected.
In the context of graph traversal, what does 'backtracking' refer to in Depth-First Search (DFS)?
Skipping certain branches of the graph to improve efficiency.
Returning to the parent node after exploring all descendants of a node.
Using a heuristic function to guide the search towards the goal node.
Revisiting already explored nodes to find alternative paths.
In a social network represented as a graph, what does the degree of a vertex signify?
The user's privacy settings.
The number of groups the user belongs to.
The number of friends or connections a user has.
The user's influence score.