Graphs: A Comprehensive Guide for Data Structures and Algorithms

Question 1

Which of the following algorithms is specifically designed for finding the shortest path in a graph?

Accepted Answer

Dijkstra's algorithm

Answer

Breadth-first search (BFS)

Answer

Depth-first search (DFS)

Answer

Topological sort

Question 2

Which of the following is a drawback of representing graphs using adjacency lists?

Accepted Answer

Requires more memory than adjacency matrices.

Answer

Efficient for graphs with few edges.

Answer

Simple to implement.

Answer

Can represent directed graphs.

Question 3

What is the time complexity of a Breadth First Search (BFS) traversal on a graph with V vertices and E edges?

Accepted Answer

O(V + E)

Answer

O(V)

Answer

O(E)

Answer

O(V * E)

Question 4

What is the key distinction between directed and undirected graphs?

Accepted Answer

Edges in directed graphs have a specified direction, while edges in undirected graphs do not

Answer

Undirected graphs have weighted edges, while directed graphs do not

Answer

Directed graphs represent one-way relationships, while undirected graphs represent two-way relationships

Answer

Undirected graphs are more common in practice than directed graphs

Question 5

What is the adjacency matrix representation of a graph with n nodes?

Accepted Answer

A square matrix of size n x n, where each entry represents the weight of the edge between the corresponding nodes

Answer

A list of lists, where each sublist represents the edges connected to a particular node

Answer

A hash table, where keys are nodes and values are the list of their connected edges

Answer

A tree structure, where each node represents a vertex and each branch represents an edge

Question 6

Which method is commonly used to detect cycles in a graph?

Accepted Answer

Depth First Search (DFS)

Answer

Breadth First Search (BFS)

Answer

Dijkstra's algorithm

Answer

Kruskal's algorithm

Question 7

What is the primary application of topological sorting in graph theory?

Accepted Answer

Determining the order in which tasks should be completed without creating circular dependencies

Answer

Detecting cycles in a graph

Answer

Calculating the shortest path between two nodes in a graph

Answer

Representing hierarchical data structures

Question 8

Which of the following is NOT a valid representation of a graph?

Accepted Answer

Vertex list

Answer

Adjacency list

Answer

Adjacency matrix

Answer

Edge list

Question 9

What is the time complexity of a depth-first search (DFS) on a graph with V vertices and E edges?

Accepted Answer

O(V+E)

Answer

O(E)

Answer

O(V^2)

Answer

O(V*logV)

Question 10

What is the purpose of a directed graph?

Accepted Answer

To represent relationships where directionality is important

Answer

To represent relationships where symmetry is required

Answer

To represent relationships where self-loops are not allowed

Answer

To represent relationships where multiple edges between vertices are not allowed

Question 11

What is the minimum number of colors required to color a graph with V vertices such that no two adjacent vertices have the same color?

Accepted Answer

Chromatic number of the graph

Answer

V

Answer

E

Answer

V+E

Question 12

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

Accepted Answer

Dijkstra's algorithm

Answer

Breadth-first search

Answer

Kruskal's algorithm

Answer

Floyd-Warshall algorithm

Question 13

What is the topological sort of a directed acyclic graph (DAG)?

Accepted Answer

An ordering of vertices such that for every directed edge (u, v), u comes before v in the ordering

Answer

An ordering of vertices such that for every directed edge (u, v), v comes before u in the ordering

Answer

An ordering of vertices such that there are no directed edges between adjacent vertices

Answer

An ordering of vertices such that the graph is acyclic

Question 14

Which of the following is a valid application of a minimum spanning tree (MST)?

Accepted Answer

Designing a network with minimal total cable length

Answer

Finding the shortest path between all pairs of vertices in a graph

Answer

Determining the maximum number of edges required to connect all vertices in a graph

Answer

Identifying the most influential nodes in a social network

Question 15

What is the significance of a Hamiltonian cycle in a graph?

Accepted Answer

It represents a path that visits every vertex in the graph exactly once and returns to the starting vertex

Answer

It represents the shortest possible path that visits every vertex in the graph

Answer

It represents the path with the maximum total weight in a weighted graph

Answer

It represents the path that minimizes the number of edges traversed in a graph

Question 16

What is the minimum number of colors needed to color a graph such that adjacent vertices have different colors?

Accepted Answer

Chromatic number

Answer

Dominating number

Answer

Independence number

Answer

Clique number

Question 17

What is the Hamiltonian circuit problem?

Accepted Answer

Finding a cycle that visits every vertex exactly once

Answer

Finding the shortest path between two vertices

Answer

Finding the maximum clique in a graph

Answer

Finding the minimum spanning tree of a graph

Question 18

Which of the following is a common application of minimum spanning trees?

Accepted Answer

Network design

Answer

Clustering

Answer

Image segmentation

Answer

Scheduling

Question 19

In a directed graph, what is the definition of strongly connected components?

Accepted Answer

Sets of vertices where every vertex can be reached from every other vertex by following the direction of edges.

Answer

Sets of vertices that form a cycle in an undirected graph.

Answer

Clusters of vertices with the same degree.

Answer

Paths from a source vertex to all other vertices in the graph.

Question 20

Which of the following data structures is commonly used to represent a graph?

Accepted Answer

Adjacency List

Answer

Array

Answer

Linked List

Answer

Queue

Question 21

Select the traversal algorithm that systematically visits every node in a graph, starting from a specific node, and explores all its adjacent nodes before moving on:

Accepted Answer

Breadth-First Search (BFS)

Answer

Depth-First Search (DFS)

Answer

Dijkstra's Algorithm

Answer

Floyd-Warshall Algorithm

Question 22

Which of the following is **not** a common application of graphs?

Accepted Answer

Linear regression

Answer

Social networks

Answer

Routing algorithms

Answer

Scheduling problems

Question 23

In a directed graph, the edges exhibit a specific characteristic. What is this characteristic?

Accepted Answer

Direction

Answer

Weight

Answer

Label

Answer

Capacity

Question 24

Which type of graph assigns a numerical value to each edge?

Accepted Answer

Weighted graph

Answer

Unweighted graph

Answer

Labeled graph

Answer

Directed graph

Question 25

In an adjacency list representation of a graph, which data structure is employed to store the adjacency information?

Accepted Answer

List

Answer

Tuple

Answer

Dictionary

Answer

Array

Question 26

Which property is associated with a planar graph?

Accepted Answer

It can be drawn on a plane without any edge crossings

Answer

It is a connected graph

Answer

It has an Eulerian cycle

Answer

It has a Hamiltonian path

Question 27

In graph theory, what is the relationship between the degree of a vertex and the number of edges connected to it?

Accepted Answer

The degree of a vertex is the same as the number of edges connected to it.

Answer

The degree of a vertex is always higher than the number of edges connected to it.

Answer

The number of edges connected to a vertex is always an even number.

Answer

The degree of a vertex is the sum of the weights of all edges connected to it.

Question 28

Which data structure is most commonly used for representing graphs?

Accepted Answer

Dictionary

Answer

Array

Answer

Linked List

Answer

Tree

Question 29

What is the asymptotic time complexity of a Breadth-First Search (BFS) on a graph with V vertices and E edges?

Accepted Answer

O(V + E)

Answer

O(V)

Answer

O(E log V)

Answer

O(E^V)

Question 30

Which traversal algorithm always visits a node before any of its children?

Accepted Answer

Depth-First Search (DFS)

Answer

Breadth-First Search (BFS)

Answer

Dijkstra's Algorithm

Answer

Prim's Algorithm

Question 31

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

Accepted Answer

Connecting all nodes with the minimum total edge weight

Answer

Finding the shortest path between two nodes

Answer

Determining the number of cycles in the graph

Answer

Finding the longest path in the graph

Question 32

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

Accepted Answer

Dijkstra's Algorithm

Answer

Bellman-Ford Algorithm

Answer

Prim's Algorithm

Answer

Kruskal's Algorithm

Question 33

What is a topological ordering of a directed acyclic graph (DAG)?

Accepted Answer

An ordering of the nodes such that every directed edge points to a node that comes later in the ordering

Answer

An ordering of the nodes such that every directed edge points to a node that comes earlier in the ordering

Answer

An ordering of the nodes such that there are no cycles in the graph

Answer

An ordering of the nodes such that the sum of edge weights is minimized

Question 34

What is the key difference between weighted and unweighted graphs?

Accepted Answer

Weighted graphs have edge weights, while unweighted graphs do not

Answer

Unweighted graphs have edge weights, while weighted graphs do not

Answer

Weighted graphs have more edges than unweighted graphs

Answer

Unweighted graphs have more nodes than weighted graphs

Question 35

What is a Hamiltonian cycle in an undirected graph?

Accepted Answer

A path that visits every vertex exactly once and ends at the starting vertex

Answer

A path that visits every vertex exactly once

Answer

A cycle that visits every vertex exactly once

Answer

A cycle that visits every edge exactly once

Question 36

Which of the following is NOT an application of graphs?

Accepted Answer

Implementing search engines

Answer

Modeling social networks

Answer

Solving optimization problems

Answer

Representing geographical maps

Question 37

What is the key difference between an undirected and a directed graph?

Accepted Answer

Edges in an undirected graph have no direction, while edges in a directed graph do

Answer

Graphs with cycles are undirected, while graphs without cycles are directed

Answer

Undirected graphs can represent relationships, while directed graphs can represent flows

Answer

Directed graphs have weights, while undirected graphs do not

Question 38

Which traversal method would you typically use to find all the nodes reachable from a given starting node in an undirected graph?

Accepted Answer

Breadth-first search (BFS)

Answer

Depth-first search (DFS)

Answer

Topological sort

Answer

Union-find

Question 39

What is the term used to describe the minimum number of colors needed to color a graph such that no two adjacent nodes have the same color?

Accepted Answer

chromatic number

Answer

girth

Answer

order

Answer

size

Question 40

What is the time complexity of finding the minimum spanning tree of an undirected graph with 'V' vertices and 'E' edges using Kruskal's algorithm?

Accepted Answer

O(E log V)

Answer

O(V)

Answer

O(E^2)

Answer

O(V^2)

Question 41

In which domain are graphs typically NOT employed?

Accepted Answer

Numerical Analysis

Answer

Social Networks

Answer

Routing

Answer

Scheduling

Question 42

What is the typical time complexity of performing a breadth-first search (BFS) on a simple (unweighted) graph with V vertices and E edges?

Accepted Answer

O(V + E)

Answer

O(V log V)

Answer

O(E log V)

Answer

O(E^2)

Question 43

Which of the following is a characteristic of a directed graph?

Accepted Answer

Edges have a defined direction

Answer

It is free of cycles

Answer

Vertices can only be reached through one incoming edge

Answer

Edges are always weighted

Question 44

What does a minimum spanning tree (MST) of a weighted graph represent?

Accepted Answer

A subset of edges that connects all vertices with the minimum possible total weight

Answer

A path that visits each vertex exactly once

Answer

A tree with the maximum number of edges

Answer

A collection of edges that form a closed loop

Question 45

Which of the following algorithms is commonly used to find the shortest weighted path between two vertices in a weighted graph?

Accepted Answer

Dijkstra's algorithm

Answer

Prim's algorithm

Answer

Breadth-first search

Answer

Kruskal's algorithm

Question 46

What is the primary difference between a weighted and an unweighted graph?

Accepted Answer

Weighted graphs assign values (weights) to their edges, while unweighted graphs do not

Answer

The edges in weighted graphs are always visible, while the edges in unweighted graphs are hidden

Answer

Unweighted graphs have more nodes than weighted graphs

Answer

Weighted graphs have directed edges, while unweighted graphs do not

Question 47

Which of the following real-world applications commonly utilizes graphs as their underlying data structure?

Accepted Answer

Social networks, route planning systems, and optimization algorithms

Answer

Databases, spreadsheets, and word processors

Answer

Video games, graphics editors, and music players

Answer

Operating systems, databases, and programming languages

Question 48

What is a key purpose of using a depth-first search (DFS) on a graph?

Accepted Answer

To explore the graph's structure by traversing as far as possible along each branch before backtracking

Answer

To identify the shortest path between two specific vertices

Answer

To count the number of vertices and edges in the graph

Answer

To determine whether the graph contains any cycles

Question 49

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

Accepted Answer

Binary search

Answer

Depth-first search

Answer

Breadth-first search

Answer

Topological sort

Question 50

What characterizes a Hamiltonian cycle in a graph?

Accepted Answer

It is a path that visits every vertex exactly once and returns to the starting vertex

Answer

It is a cycle that passes through all edges of the graph

Answer

It is a set of edges that forms a tree structure

Answer

It is the path with the minimum total distance