Master Graph Algorithms: Enhance Your Computer Science Skills

Question 1

What is the time complexity of traversing a graph using depth-first search?

Accepted Answer

O(V + E)

Answer

O(V)

Answer

O(E)

Answer

O(V^2)

Question 2

What is the primary goal of a minimum spanning tree algorithm?

Accepted Answer

To find a set of edges connecting all nodes in a graph with minimum total weight

Answer

To find the shortest path between two nodes

Answer

To find the largest connected component in a graph

Answer

To detect cycles in a graph

Question 3

What is the key distinction between directed and undirected graphs?

Accepted Answer

Directed graphs have edges with direction, while undirected graphs do not

Answer

Undirected graphs have edges with direction, while directed graphs do not

Answer

Directed graphs have weighted edges, while undirected graphs do not

Answer

Undirected graphs have weighted edges, while directed graphs do not

Question 4

Which of the following is NOT a method of traversing a graph?

Accepted Answer

Dijkstra's algorithm

Answer

Depth-first search

Answer

Breadth-first search

Answer

Topological sort

Question 5

What is the fundamental difference between graphs and trees?

Accepted Answer

Graphs can have cycles, while trees cannot

Answer

Trees can have cycles, while graphs cannot

Answer

Graphs are always connected, while trees are not

Answer

Trees are always connected, while graphs are not

Question 6

Which algorithm can be used to find the shortest path between two vertices in a weighted graph?

Accepted Answer

Dijkstra's algorithm

Answer

Kruskal's algorithm

Answer

Prim's algorithm

Answer

Floyd-Warshall algorithm

Question 7

What is the maximum degree of a regular graph with N vertices?

Accepted Answer

N/2

Answer

N/3

Answer

N/4

Answer

N/5

Question 8

A Hamiltonian path is:

Accepted Answer

A path that visits every vertex in a graph exactly once

Answer

A path that visits every edge in a graph exactly once

Answer

A cycle that visits every vertex in a graph exactly once

Answer

A cycle that visits every edge in a graph exactly once

Question 9

Which data structure is typically used to represent graphs?

Accepted Answer

Graph

Answer

LinkedList

Answer

Array

Answer

Tree

Question 10

What is the time complexity of the Floyd-Warshall algorithm for finding all-pair shortest paths in a graph?

Accepted Answer

O(V^3)

Answer

O(V)

Answer

O(V log V)

Answer

O(E log V)

Question 11

Dijkstra's algorithm has a notable limitation. Explain this constraint and discuss how it impacts the algorithm's real-world applications.

Accepted Answer

Dijkstra's algorithm cannot handle negative edge weights.

Answer

Dijkstra's algorithm is limited to unweighted graphs.

Answer

Dijkstra's algorithm requires a complete graph with all possible edges.

Answer

Dijkstra's algorithm always finds the shortest path, regardless of the graph's structure.

Question 12

In route planning, which graph algorithm is used to determine the most efficient path for a delivery vehicle?

Accepted Answer

Dijkstra's Algorithm

Answer

Depth-First Search (DFS)

Answer

Breadth-First Search (BFS)

Answer

Kruskal's Algorithm

Question 13

In the real world, when would you use a minimum spanning tree algorithm?

Accepted Answer

Designing a telecommunications network

Answer

Finding the shortest path between two cities

Answer

Identifying clusters or communities within a social network

Question 14

Which of the following algorithms can be used to traverse a graph depth-first?

Accepted Answer

Depth-First Search (DFS)

Answer

Breadth-First Search (BFS)

Answer

Bellman-Ford algorithm

Answer

Dijkstra's algorithm

Question 15

Which algorithm is specifically designed to find the shortest path between two nodes in a weighted graph?

Accepted Answer

Dijkstra's algorithm

Answer

Floyd-Warshall algorithm

Answer

Kruskal's algorithm

Answer

Bellman-Ford algorithm

Question 16

When finding the minimum spanning tree of a graph, which of these algorithms is commonly used?

Accepted Answer

Kruskal's algorithm

Answer

Bellman-Ford algorithm

Answer

Floyd-Warshall algorithm

Answer

Dijkstra's algorithm

Question 17

Which of the following conditions must be met for a graph to have an Eulerian cycle?

Accepted Answer

The graph is connected and all vertices have even degrees.

Answer

The graph is disconnected and all vertices have even degrees.

Answer

The graph is connected and all vertices have odd degrees.

Question 18

In the context of computer science, which of these is a common application of graph algorithms?

Accepted Answer

Routing in computer networks

Answer

Solving differential equations

Answer

Sorting arrays

Answer

Determining the primality of numbers

Question 19

Which of the following concepts is not directly related to the study of graph algorithms?

Accepted Answer

Hashing

Answer

Shortest path optimization

Answer

Planarity

Answer

Network flow

Question 20

Which algorithm is most efficient for finding all pairs of shortest paths in a graph?

Accepted Answer

Floyd-Warshall algorithm

Answer

Prim's algorithm

Answer

Dijkstra's algorithm

Answer

Bellman-Ford algorithm

Question 21

Which data structure is most suitable for representing a graph?

Accepted Answer

Adjacency list

Answer

Array

Answer

Linked list

Answer

Binary tree

Question 22

What is the time complexity of Depth-First Search (DFS)?

Accepted Answer

O(V + E)

Answer

O(V)

Answer

O(E)

Answer

O(V^2)

Question 23

What is the purpose of a Minimum Spanning Tree (MST)?

Accepted Answer

To connect all nodes in a graph with minimum total edge weight

Answer

To find the longest path in a graph

Answer

To determine if a graph is connected

Question 24

Which of the following is NOT a property of a bipartite graph?

Accepted Answer

Every vertex has degree at least 2

Answer

No two vertices in the same set are adjacent

Answer

The graph is acyclic

Answer

The graph can be divided into two disjoint sets of vertices

Question 25

What is the edge connectivity of a graph with n vertices and m edges?

Accepted Answer

The minimum number of edges that must be removed to disconnect the graph

Answer

The maximum number of edges that can be added to the graph without creating a cycle

Answer

The number of connected components in the graph

Question 26

What is the Kruskal's algorithm used for?

Accepted Answer

Finding a Minimum Spanning Tree (MST)

Answer

Topological sorting

Answer

Finding the shortest path between two nodes

Answer

Detecting cycles in a graph

Question 27

What is the chromatic number of a graph?

Accepted Answer

The minimum number of colors needed to color the vertices of a graph such that no two adjacent vertices have the same color

Answer

The maximum number of edges that can be added to the graph without creating a cycle