In the worst-case scenario, what is the time complexity of the Floyd-Warshall algorithm for a graph with 'V' vertices?
O(E log V)
O(V^3)
O(V log V)
O(V^2)
In a graph coloring problem, what scenario leads to the requirement of an additional color?
Removing an edge between two vertices with the same color.
Adding a new vertex and connecting it to all existing vertices.
Adding an edge between two vertices with different colors.
Adding a new vertex and connecting it to an existing vertex.
How does the Bellman-Ford algorithm handle negative weight cycles when determining shortest paths?
It utilizes a separate algorithm to handle negative weight cycles after executing the main algorithm.
It ignores negative weight cycles and finds the shortest path regardless.
It modifies the edge weights to eliminate negative cycles before finding the shortest path.
It detects and reports the existence of negative weight cycles, indicating that a shortest path may not exist.
How does the A* algorithm handle situations where a more promising path to a previously explored node is discovered?
It ignores the new path and continues with the existing path.
It updates the cost of the node and re-evaluates its neighbors.
It restarts the search from the start node with the updated information.
It marks the node as visited and does not consider it again.
What is the relationship between A* search and Dijkstra's algorithm?
A* and Dijkstra's algorithm are entirely unrelated.
Dijkstra's algorithm is a special case of A* search.
A* is only applicable to unweighted graphs, while Dijkstra's algorithm works for weighted graphs.
A* is a generalization of Dijkstra's algorithm.
Which of the following data structures is commonly used to implement the priority queue in A* search?
Linked list
Binary heap
Queue
Stack
Johnson's algorithm improves the efficiency of finding all-pairs shortest paths in which type of graph?
Sparse graphs with negative edge weights
Dense graphs with positive edge weights
Directed acyclic graphs (DAGs)
Unweighted graphs
In the worst case, how many iterations does the Bellman-Ford algorithm need to guarantee finding the shortest path?
V - 1
E
E - 1
V
Which of the following statements is NOT TRUE about a graph with a Hamiltonian cycle?
The graph is planar.
The graph is connected.
The number of vertices is greater than or equal to 3.
Every vertex has a degree of at least 2.
What is an advantage of using a Fibonacci heap implementation for Dijkstra's algorithm?
It improves the time complexity for sparse graphs.
It reduces the space complexity of the algorithm.
It simplifies the implementation of the algorithm.
It allows the algorithm to handle negative edge weights.