Which algorithm is typically used to find the shortest path in a weighted graph where edge weights are non-negative?
Dijkstra's Algorithm
Depth First Search (DFS)
Breadth First Search (BFS)
Bellman-Ford Algorithm
If every vertex in a graph has an even degree, what can we conclude about the graph?
It must be a tree.
It must have an Eulerian cycle.
It must be directed.
It must be bipartite.
In an undirected graph with 5 vertices, what is the maximum number of edges you can add without creating a cycle?
5
4
10
6
Removing a vertex from a graph also requires you to remove:
All vertices connected to it.
All cycles in the graph.
The vertex with the highest degree.
All edges connected to it.
You remove an edge from a connected graph. What is a possible consequence of this action?
The number of edges and vertices in the graph will decrease.
The number of cycles in the graph will always decrease.
The graph may become disconnected.
The graph will always become disconnected.
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 social network represented as a graph, what does the degree of a vertex signify?
The user's influence score.
The number of groups the user belongs to.
The user's privacy settings.
The number of friends or connections a user has.
In a connected graph, a path that visits every edge exactly once is known as:
Hamiltonian Path
Eulerian Path
Critical Path
Shortest 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.
Both DFS and BFS have the same efficiency for this task.
Depth-First Search (DFS)
A cycle in a graph that is not a simple cycle (visits a vertex more than once) is called a:
Trail
Circuit
Closed Walk
Path