Graph Algorithms MCQs

This comprehensive set of Graph Algorithms MCQs is designed to cover all essential topics required for success in exams related to graph theory and algorithm design. Focused on key subjects such as graph representations, traversal techniques, shortest path algorithms, minimum spanning trees, and network flow, these MCQs are crafted to help students build a strong foundation in graph algorithms and their applications.

Who should practice Graph Algorithms MCQs?

Students preparing for computer science, data structures, or algorithms courses that include graph theory concepts.
Individuals aiming to strengthen their understanding of various graph representations (adjacency list, adjacency matrix) and traversal methods (BFS, DFS).
Candidates preparing for competitive programming or coding interviews that assess knowledge of graph algorithms and problem-solving skills.
Learners interested in mastering key algorithms such as Dijkstra’s, Bellman-Ford, Prim’s, and Kruskal’s.
Professionals focused on improving their skills in optimization problems, network design, and analyzing graph-based data structures.
Suitable for all aspirants seeking to enhance their knowledge and performance in graph algorithms for academic or professional success.

1. What is the time complexity of Depth-First Search (DFS) in a graph?

A) O(V)
B) O(V + E)
C) O(E)
D) O(V^2)

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2. Which algorithm is used to find the shortest path in a graph with non-negative weights?

A) Depth-First Search
B) Dijkstra’s Algorithm
C) Bellman-Ford Algorithm
D) Prim’s Algorithm

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3. What does the “V” represent in the context of graphs?

A) Variables
B) Vertices
C) Values
D) Vectors

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4. In a directed graph, what is the term for a path that visits a vertex more than once?

A) Cycle
B) Circuit
C) Path
D) Loop

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5. Which of the following algorithms can be used to find a Minimum Spanning Tree (MST)?

A) Kruskal’s Algorithm
B) Dijkstra’s Algorithm
C) Bellman-Ford Algorithm
D) A* Search Algorithm

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6. What is the primary data structure used to implement a graph?

A) Array
B) Linked List
C) Tree
D) Adjacency List

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7. In which case does the Bellman-Ford algorithm fail?

A) Negative weight cycles
B) Positive weights
C) Directed graphs
D) Undirected graphs

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8. What type of graph is a tree?

A) Connected and cyclic
B) Connected and acyclic
C) Disconnected and cyclic
D) Disconnected and acyclic

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9. What is the main advantage of using Prim’s Algorithm over Kruskal’s Algorithm?

A) It works better with sparse graphs
B) It has a simpler implementation
C) It can handle negative weights
D) It is more efficient for dense graphs

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10. Which traversal method can be used to determine if a graph is bipartite?

A) Depth-First Search
B) Breadth-First Search
C) Both A and B
D) None of the above

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11. In graph theory, what is the degree of a vertex?

A) The number of edges incident to it
B) The number of vertices in the graph
C) The distance from the vertex to another vertex
D) The number of paths from the vertex

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12. What does a topological sort of a directed acyclic graph (DAG) represent?

A) The shortest path
B) The order of processing
C) The longest path
D) The minimum spanning tree

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13. Which data structure is commonly used to implement Dijkstra’s algorithm?

A) Queue
B) Stack
C) Priority Queue
D) Linked List

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14. What is the worst-case time complexity of Kruskal’s algorithm?

A) O(E log V)
B) O(V^2)
C) O(V + E)
D) O(E^2)

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15. Which of the following algorithms can detect negative weight cycles?

A) Dijkstra’s Algorithm
B) Bellman-Ford Algorithm
C) Prim’s Algorithm
D) Kruskal’s Algorithm

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16. In an undirected graph, what is the maximum number of edges?

A) V
B) V^2
C) V(V-1)/2
D) E

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17. Which algorithm is used to find strongly connected components in a directed graph?

A) Dijkstra’s Algorithm
B) Bellman-Ford Algorithm
C) Tarjan’s Algorithm
D) Kruskal’s Algorithm

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18. In a weighted graph, what is the purpose of the weights?

A) To represent distances or costs
B) To determine connectivity
C) To identify vertices
D) To define cycles

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19. Which of the following graphs contains cycles?

A) Tree
B) Acyclic Graph
C) Directed Graph
D) Cyclic Graph

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20. In graph terminology, what is an “edge”?

A) A connection between two vertices
B) A single vertex
C) A path between two vertices
D) A loop in a graph

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21. Which method is typically used for breadth-first traversal of a graph?

A) Stack
B) Queue
C) Array
D) Linked List

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22. What is the time complexity of Breadth-First Search (BFS)?

A) O(V^2)
B) O(E)
C) O(V + E)
D) O(V log V)

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23. In which scenario is BFS preferred over DFS?

A) When the graph is very deep
B) When finding the shortest path in an unweighted graph
C) When the graph is very wide
D) When the graph is cyclic

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24. What is the space complexity of the adjacency list representation of a graph?

A) O(V)
B) O(V + E)
C) O(E)
D) O(V^2)

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25. Which algorithm finds the minimum spanning tree of a graph?

A) Dijkstra’s Algorithm
B) Kruskal’s Algorithm
C) Bellman-Ford Algorithm
D) Floyd-Warshall Algorithm

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26. What does “greedy algorithm” mean in the context of graph algorithms?

A) An algorithm that always chooses the most optimal solution
B) An algorithm that makes the locally optimal choice at each step
C) An algorithm that explores all possible paths
D) An algorithm that requires backtracking

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27. In a complete graph, how many edges are there?

A) V
B) V – 1
C) V(V – 1)/2
D) V^2

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28. What is a leaf node in a tree structure?

A) A node with two children
B) A node with no children
C) A node with one child
D) A node that connects two trees

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29. Which of the following is NOT a characteristic of a tree?

A) Acyclic
B) Connected
C) Contains cycles
D) Has a root node

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30. In graph theory, what does the term “connected” mean?

A) All vertices are reachable from one another
B) There are no cycles
C) There is at least one edge
D) There are multiple components

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31. Which of the following can be represented as a graph?

A) A social network
B) A computer network
C) A transportation system
D) All of the above

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32. What is the primary characteristic of a bipartite graph?

A) It has only two vertices
B) It can be colored with two colors
C) It is always complete
D) It contains cycles

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33. Which data structure is typically used to implement Kruskal’s algorithm?

A) Stack
B) Queue
C) Union-Find
D) Adjacency List

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34. In a directed graph, what does it mean for an edge to be “directed”?

A) It has no weight
B) It has a specified start and end vertex
C) It connects two vertices
D) It is bidirectional

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35. What is a “path” in graph terminology?

A) A route between two vertices
B) A single edge
C) A set of vertices
D) A cycle

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36. What is the primary use of the Floyd-Warshall algorithm?

A) Finding the shortest path in unweighted graphs
B) Finding the shortest path between all pairs of vertices
C) Finding minimum spanning trees
D) Detecting cycles

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37. Which of the following best describes a “cycle” in a graph?

A) A closed path with no repeated edges
B) A closed path with repeated edges
C) A path that starts and ends at the same vertex
D) A connected graph

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38. What is the purpose of the “Union-Find” data structure?

A) To implement depth-first search
B) To find cycles in a graph
C) To manage disjoint sets
D) To store graph edges

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39. Which algorithm is primarily used for network flow problems?

A) Dijkstra’s Algorithm
B) Bellman-Ford Algorithm
C) Ford-Fulkerson Algorithm
D) Kruskal’s Algorithm

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40. What is a “subgraph”?

A) A graph that contains all vertices of another graph
B) A graph formed from a subset of vertices and edges of another graph
C) A graph with a higher number of edges
D) A graph that is disconnected

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41. What is the purpose of the A algorithm in graph theory?*

A) Finding minimum spanning trees
B) Finding the shortest path
C) Finding maximum flow
D) Finding all paths

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42. Which of the following represents a non-directed edge?

A) A → B
B) A ↔ B
C) A – B
D) Both B and C

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43. What is an adjacency matrix?

A) A matrix used to represent the weights of edges
B) A matrix that indicates the presence of edges between vertices
C) A list of vertices
D) A list of edges

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44. Which of the following graph traversal algorithms uses recursion?

A) Depth-First Search
B) Breadth-First Search
C) Dijkstra’s Algorithm
D) Prim’s Algorithm

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45. What is a connected component in a graph?

A) A set of edges
B) A subgraph in which any two vertices are connected
C) A vertex with no edges
D) A path that visits all vertices

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46. What is the key characteristic of a directed acyclic graph (DAG)?

A) It contains cycles
B) It has no directed edges
C) It has no cycles
D) It is always complete

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47. Which graph traversal method guarantees the shortest path in an unweighted graph?

A) Depth-First Search
B) Breadth-First Search
C) Dijkstra’s Algorithm
D) Bellman-Ford Algorithm

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48. What type of graph has all vertices of equal degree?

A) Complete Graph
B) Regular Graph
C) Bipartite Graph
D) Directed Graph

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49. What does the term “vertex cover” refer to in graph theory?

A) A subset of vertices covering all edges
B) A subset of edges covering all vertices
C) A path visiting all vertices
D) A disconnected subgraph

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50. In a weighted directed graph, what is a “negative cycle”?

A) A cycle where the sum of edge weights is negative
B) A cycle that does not exist
C) A cycle with zero weight
D) A cycle with positive weights

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51. Which of the following is NOT a property of a tree?

A) Has a root
B) Contains cycles
C) Connected
D) Acyclic

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52. What is the main purpose of the Kruskal’s algorithm?

A) To find the shortest path
B) To find the maximum flow
C) To find the minimum spanning tree
D) To detect cycles

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53. What type of graph is represented by an adjacency list?

A) Directed Graph
B) Undirected Graph
C) Both A and B
D) Weighted Graph

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54. What is a directed graph?

A) A graph where edges have no direction
B) A graph where edges have a specified direction
C) A graph with no edges
D) A graph with only one vertex

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55. What is the worst-case time complexity of Dijkstra’s algorithm using a priority queue?

A) O(V^2)
B) O(E log V)
C) O(V log V)
D) O(E + V)

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56. In graph theory, what is the difference between a path and a cycle?

A) A path can repeat vertices; a cycle cannot
B) A cycle must start and end at the same vertex; a path does not
C) A path must have at least one edge; a cycle can have zero edges
D) There is no difference; they are the same

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57. Which of the following is used for finding the longest path in a graph?

A) Bellman-Ford Algorithm
B) Dijkstra’s Algorithm
C) Dynamic Programming
D) There is no efficient solution

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58. What is the time complexity of detecting cycles in a directed graph using DFS?

A) O(V^2)
B) O(V + E)
C) O(E)
D) O(V log V)

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59. Which of the following statements is true about a complete graph?

A) All vertices are connected to all other vertices
B) It has a minimum number of edges
C) It cannot have more than one edge
D) It is always acyclic

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60. What is a multi-graph?

A) A graph with multiple vertices
B) A graph with parallel edges between the same vertices
C) A graph with weighted edges
D) A graph with no edges

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61. Which traversal method is optimal for finding a node’s neighbors?

A) Depth-First Search
B) Breadth-First Search
C) Random Walk
D) Nearest Neighbor

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62. In a bipartite graph, what is the characteristic of the two sets of vertices?

A) All vertices are connected to each other
B) Each vertex in one set is connected to all vertices in the other set
C) There are no edges
D) They contain the same number of vertices

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63. Which of the following is NOT a type of graph?

A) Directed
B) Undirected
C) Weighted
D) Undefined

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64. What is a flow network?

A) A graph where edges have capacities
B) A graph with negative weights
C) A tree structure
D) A complete graph

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65. Which algorithm is used for shortest path in a weighted graph with negative weights?

A) Dijkstra’s Algorithm
B) Bellman-Ford Algorithm
C) Prim’s Algorithm
D) Kruskal’s Algorithm

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66. In a weighted graph, what is the purpose of an edge weight?

A) To indicate the direction of an edge
B) To represent the cost or distance associated with traversing the edge
C) To determine the connectivity of vertices
D) To represent the number of vertices

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67. What is the significance of a root node in a tree?

A) It has no children
B) It is the starting point for traversals
C) It can be connected to multiple nodes
D) All of the above

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68. What does the term “subtree” refer to in tree data structures?

A) A graph that contains only leaves
B) A section of a tree containing a node and its descendants
C) A path from root to leaf
D) A cycle within a tree

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69. What is the difference between a tree and a graph?

A) Trees are connected; graphs can be disconnected
B) Trees do not have cycles; graphs can
C) Trees have a hierarchical structure; graphs do not
D) All of the above

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70. Which of the following algorithms is used for finding the minimum spanning tree?

A) Prim’s Algorithm
B) Dijkstra’s Algorithm
C) Bellman-Ford Algorithm
D) All of the above

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71. What is a directed acyclic graph (DAG) commonly used for?

A) Network routing
B) Job scheduling
C) Data flow representation
D) All of the above

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72. Which method can be used to solve the Traveling Salesman Problem?

A) Dijkstra’s Algorithm
B) Dynamic Programming
C) Bellman-Ford Algorithm
D) Prim’s Algorithm

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73. In a graph, what is a “source” vertex?

A) A vertex with no outgoing edges
B) A vertex with no incoming edges
C) A vertex connected to multiple vertices
D) A vertex in the middle of a path

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74. What is the primary purpose of using heuristics in graph algorithms?

A) To speed up the algorithm
B) To ensure optimal solutions
C) To reduce space complexity
D) To find all possible paths

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75. What is the key idea behind the Ford-Fulkerson method?

A) Finding cycles in a graph
B) Finding maximum flow in a flow network
C) Finding minimum spanning trees
D) Finding the shortest path

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76. In graph theory, what does “degree centrality” measure?

A) The importance of a vertex based on its connections
B) The shortest path from a vertex to another
C) The total weight of edges connected to a vertex
D) The average distance between vertices

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77. What is a “spanning tree”?

A) A tree that includes all vertices of a graph
B) A tree with the minimum number of edges
C) A cycle in a graph
D) A disconnected graph

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78. Which of the following is true about a forest?

A) It is a type of graph
B) It consists of disjoint trees
C) It contains cycles
D) Both A and B

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79. What is the function of the “visited” array in graph algorithms?

A) To track the order of traversal
B) To mark which vertices have been processed
C) To store distances from the source vertex
D) To count the number of edges

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80. Which traversal method is optimal for searching for a specific node?

A) Depth-First Search
B) Breadth-First Search
C) Both A and B
D) None of the above

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81. What is the primary use of the Edmonds-Karp algorithm?

A) Finding minimum spanning trees
B) Finding maximum flow in a flow network
C) Finding shortest paths
D) Detecting cycles

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82. Which of the following best describes a complete bipartite graph?

A) A graph where every vertex is connected to every other vertex
B) A graph where vertices can be divided into two sets, with edges only between sets
C) A graph that contains cycles
D) A disconnected graph

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83. What is the function of a heuristic in search algorithms?

A) To provide the exact solution
B) To estimate the cost of reaching the goal
C) To simplify the problem
D) To optimize space complexity

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84. What does the “backtracking” method accomplish in graph algorithms?

A) It finds cycles
B) It traverses all possible paths
C) It finds the shortest path
D) It eliminates unnecessary paths

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85. Which of the following can represent a graph with edges having weights?

A) Adjacency Matrix
B) Adjacency List
C) Edge List
D) All of the above

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86. In graph algorithms, what does “greedy” refer to?

A) Making the best local choice at each stage
B) Finding the optimal solution
C) Exhaustive search
D) Random selection

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87. What is the main drawback of Dijkstra’s algorithm?

A) It cannot handle negative weights
B) It is too slow for large graphs
C) It only works for undirected graphs
D) It requires a complete graph

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88. Which of the following graph traversal algorithms is not guaranteed to find the shortest path?

A) Dijkstra’s Algorithm
B) Bellman-Ford Algorithm
C) Depth-First Search
D) Breadth-First Search

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89. What is the time complexity of a binary tree traversal?

A) O(V)
B) O(E)
C) O(V + E)
D) O(log V)

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90. In graph theory, what is the difference between a “vertex” and an “edge”?

A) A vertex is a point; an edge is a line connecting two points
B) A vertex can be disconnected; an edge cannot
C) A vertex represents an edge; an edge represents a vertex
D) There is no difference

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91. Which algorithm can be used to solve the maximum flow problem in a flow network?

A) Dijkstra’s Algorithm
B) Kruskal’s Algorithm
C) Ford-Fulkerson Algorithm
D) Bellman-Ford Algorithm

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92. What does a “weighted graph” indicate?

A) It has no edges
B) It has edges with associated values
C) It is a directed graph
D) It is a bipartite graph

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93. Which algorithm is suitable for finding the shortest path in a grid-based graph?

A) Dijkstra’s Algorithm
B) Depth-First Search
C) A* Search Algorithm
D) Prim’s Algorithm

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94. What is the characteristic of a “regular graph”?

A) All vertices have the same degree
B) It contains cycles
C) It is always connected
D) It has at least one vertex

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95. Which of the following algorithms can find the longest path in a directed acyclic graph (DAG)?

A) Dynamic Programming
B) Dijkstra’s Algorithm
C) Bellman-Ford Algorithm
D) Prim’s Algorithm

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96. What is a “directed graph” characterized by?

A) Edges without direction
B) Edges with specified direction
C) Only one vertex
D) No edges

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97. Which algorithm is efficient for finding the shortest path in large, sparse graphs?

A) Dijkstra’s Algorithm
B) Bellman-Ford Algorithm
C) A* Search Algorithm
D) Floyd-Warshall Algorithm

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98. What is the primary purpose of the graph traversal algorithms?

A) To find the shortest path
B) To explore all vertices and edges
C) To detect cycles
D) To find minimum spanning trees

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99. What is a “bridge” in graph theory?

A) An edge that, when removed, increases the number of connected components
B) A path connecting two vertices
C) A cycle in a graph
D) A complete graph

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100. What is the characteristic of a “tree” in graph theory?

A) It is a type of graph with no cycles
B) It has exactly one path between any two vertices
C) It is always connected
D) All of the above

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