Graph Representation and Traversal: Master the Fundamentals

Question 1

Which traversal algorithm maintains a stack to track unvisited vertices?

Accepted Answer

DFS

Answer

BFS

Answer

Dijkstra's

Answer

Prim's

Question 2

In Breadth-First Search (BFS), which technique prevents revisiting previously explored vertices?

Accepted Answer

Marking

Answer

Recursion

Answer

Stacking

Answer

Queuing

Question 3

Which traversal algorithm is employed to identify the shortest path in a weighted graph?

Accepted Answer

Dijkstra's

Answer

DFS

Answer

BFS

Answer

Kruskal's

Question 4

The space complexity of an adjacency matrix representation for a graph with N vertices is:

Accepted Answer

N * N

Answer

N * (N - 1)

Answer

N

Answer

Log(N)

Question 5

In BFS, which data structure is used to manage the next vertices to be visited?

Accepted Answer

Queue

Answer

Stack

Answer

Binary tree

Answer

Hash table

Question 6

For a graph with N vertices and E edges, the time complexity of BFS is:

Accepted Answer

O(N)

Answer

O(N^2)

Answer

O(E)

Answer

O(E log N)

Question 7

In a complete graph with N vertices, the number of edges is:

Accepted Answer

N choose 2

Answer

N

Answer

N - 1

Answer

Log(N)

Question 8

For sparse graphs, which representation technique is more efficient?

Accepted Answer

Adjacency list

Answer

Adjacency matrix

Answer

Incidence matrix

Question 9

Which of the following is NOT a potential application of graph theory in computer science?

Accepted Answer

Weather forecasting

Answer

Scheduling tasks

Answer

Routing network traffic

Answer

Image processing

Question 10

In a graph traversal algorithm, what is the primary purpose of a stack data structure?

Accepted Answer

To store nodes that have been visited but not yet fully explored.

Answer

To store the shortest path from the starting node to each visited node.

Answer

To store all nodes in the graph, regardless of whether they have been visited.

Answer

To store the order in which nodes were visited.

Question 11

Which of the following data structures is most appropriate for representing a graph with a large number of edges but relatively few nodes?

Accepted Answer

Adjacency list

Answer

Adjacency matrix

Answer

Hash table

Answer

Graph database

Question 12

What is a potential disadvantage of using a dense matrix to represent a graph with a large number of nodes?

Accepted Answer

High memory consumption

Answer

High computational complexity

Answer

Difficult to update

Answer

Inefficient for representing sparse graphs

Question 13

Which of the following algorithms is used to find the shortest path between all pairs of nodes in a graph?

Accepted Answer

Floyd-Warshall algorithm

Answer

Dijkstra's algorithm

Answer

Prim's algorithm

Answer

Kruskal's algorithm

Question 14

What is a primary application of minimum spanning tree algorithms?

Accepted Answer

Network design

Answer

Clustering

Answer

Image segmentation

Answer

Shortest path finding

Question 15

Which of the following is a key advantage of using an adjacency matrix to represent a graph?

Accepted Answer

Simplified implementation of weighted edges

Answer

Improved traversal speed

Answer

Reduced memory consumption

Answer

Ease of implementation

Question 16

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

Accepted Answer

O(V)

Answer

O(V^2)

Answer

O(E)

Answer

O(E log V)

Question 17

Which of the following is a valid application of a breadth-first search (BFS) traversal?

Accepted Answer

Determining if a graph is connected

Answer

Discovering the shortest path between two vertices

Answer

Identifying all cycles within a graph

Answer

Finding the minimum spanning tree of a graph

Question 18

For a graph with V vertices and E edges, which graph representation requires the least memory storage?

Accepted Answer

Adjacency list

Answer

Adjacency matrix

Answer

Incidence matrix

Answer

Edge list

Question 19

Which traversal technique guarantees to visit all vertices and edges of a connected graph exactly once?

Accepted Answer

Eulerian traversal

Answer

Depth-first search with backtracking

Answer

Breadth-first search with backtracking

Answer

Hamiltonian traversal

Question 20

In a depth-first search, what is the primary purpose of a stack data structure?

Accepted Answer

Recording the path from the starting vertex

Answer

Storing visited vertices

Answer

Storing unvisited vertices

Answer

Maintaining the distance from the starting vertex

Question 21

Which limitation is associated with the adjacency list representation of a graph?

Accepted Answer

Unsuitability for sparse graphs

Answer

Inability to represent weighted edges

Answer

Complexity in implementation

Answer

Requirement for more memory than other representations

Question 22

For a graph with a cycle, which traversal technique is most efficient for cycle detection?

Accepted Answer

Depth-first search

Answer

Breadth-first search

Answer

Dijkstra's algorithm

Answer

Bellman-Ford algorithm

Question 23

What is a fundamental difference between directed and undirected graphs?

Accepted Answer

Directed edges have a source and destination vertex, while undirected edges do not

Answer

Directed edges have weights, while undirected edges do not

Answer

Undirected graphs allow cycles, while directed graphs do not

Answer

Undirected graphs have a higher edge density than directed graphs

Question 24

Which of the following represents a directed graph using an adjacency matrix?

Accepted Answer

A square matrix of 0s and 1s, where 1 indicates an edge from row to column

Answer

A list of lists where each element represents a node, and each nested list contains its neighbors

Answer

A dictionary of dictionaries where each key is a node, and the value is another dictionary of neighbors and edge weights

Answer

A set of tuples where each tuple represents an edge

Question 25

Which graph traversal algorithm utilizes a queue data structure?

Accepted Answer

BFS

Answer

DFS

Answer

Dijkstra's algorithm

Answer

Bellman-Ford algorithm

Question 26

What is a key advantage of using an adjacency list over an adjacency matrix for representing sparse graphs?

Accepted Answer

Reduced memory consumption

Answer

Faster traversal

Answer

Easier edge addition or removal

Answer

More efficient handling of graphs with numerous nodes

Question 27

What is the purpose of employing a disjoint-set data structure in graph algorithms?

Accepted Answer

Representing connected components

Answer

Storing shortest paths between nodes

Answer

Tracking visited nodes

Answer

Verifying for cycles in a graph

Question 28

Which technique can be employed to identify strongly connected components in an undirected graph using DFS?

Accepted Answer

Two DFS traversals are necessary: one on the original graph and one on its transpose.

Accepted Answer

Kosaraju's algorithm, a modified version of DFS, can be used to identify strongly connected components.

Answer

A single DFS traversal can identify all strongly connected components.

Answer

DFS cannot be used to identify strongly connected components in undirected graphs.

Question 29

Determine 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(V * E)

Answer

O(E * log V)

Answer

O(V^2)

Question 30

Which traversal method is employed to identify the shortest path between two vertices in an unweighted graph?

Accepted Answer

Breadth-first search (BFS)

Answer

Depth-first search (DFS)

Answer

Dijkstra's algorithm

Answer

Bellman-Ford algorithm

Question 31

In a breadth-first search (BFS) algorithm, which data structure is utilized for queue implementation?

Accepted Answer

Queue

Answer

Stack

Answer

Heap

Answer

Linked list

Question 32

Identify the advantage of using an adjacency list to represent a sparse graph.

Accepted Answer

Efficient memory usage

Answer

Faster insertion and deletion of edges

Answer

Simplified graph traversal

Answer

Support for weighted edges

Question 33

What is the primary purpose of performing a topological sort on a directed acyclic graph (DAG)?

Accepted Answer

Arrange vertices in an order that respects dependencies

Answer

Identify the longest path in the graph

Answer

Detect cycles within the graph

Answer

Minimize the number of edges in the graph

Question 34

Which algorithm can be employed to find strongly connected components (SCCs) in a directed graph?

Accepted Answer

Depth-first search (DFS)

Answer

Breadth-first search (BFS)

Answer

Kruskal's algorithm

Answer

Prim's algorithm

Question 35

Identify a limitation of Dijkstra's algorithm.

Accepted Answer

Finds only the shortest path from a single source vertex

Answer

Handles negative edge weights

Answer

Requires the graph to be acyclic

Answer

High time complexity for large graphs

Question 36

What's the time complexity of depth-first search (DFS) 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^2)

Question 37

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

Accepted Answer

O(V + E)

Answer

O(V^2)

Answer

O(E log V)

Answer

O(2^V)

Question 38

Which data structure is used to represent a graph as a collection of vertices and edges, where each vertex is associated with a list of its adjacent vertices?

Accepted Answer

Adjacency list

Answer

Array

Answer

Stack

Answer

Hash table

Question 39

In a graph represented using an adjacency matrix, what is the time complexity of finding all adjacent vertices of a given vertex?

Accepted Answer

O(1)

Answer

O(log n)

Answer

O(n^2)

Answer

O(n)

Question 40

Which graph traversal algorithm prioritizes visiting all the vertices at a given level before moving to the next level?

Accepted Answer

Breadth-first search (BFS)

Answer

Dijkstra's algorithm

Answer

Kruskal's algorithm

Answer

Depth-first search (DFS)

Question 41

In a DFS traversal, which data structure is typically used to keep track of visited vertices?

Accepted Answer

Stack

Answer

Queue

Answer

Linked list

Answer

Array

Question 42

Which traversal method can be used to determine if a graph contains any cycles?

Accepted Answer

Depth First Search (DFS)

Answer

Breadth First Search (BFS)

Answer

Bellman-Ford algorithm

Answer

Dijkstra's algorithm

Question 43

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

Accepted Answer

Adjacency matrix with all edge weights set to 1

Answer

Incidence matrix with edge weights encoded in the matrix values

Answer

Adjacency list with edge weights stored in a separate array

Answer

Edge list with edge weights included

Question 44

Which data structure is used to manage the order of vertices to be visited during a BFS traversal?

Accepted Answer

Queue

Answer

Hash table

Answer

Binary search tree

Answer

Stack

Question 45

Which data structure is typically utilized for representing graphs?

Accepted Answer

Adjacency List or Adjacency Matrix

Answer

Queue

Answer

Hash Table

Answer

Binary Tree

Question 46

In a Depth-First Search (DFS) traversal, which data structure is commonly used to track visited vertices?

Accepted Answer

Stack

Answer

Linked List

Answer

Array

Answer

Queue

Question 47

Which algorithm is used for topological sorting?

Accepted Answer

Depth-First Search (DFS) with backtracking

Answer

Kruskal's Algorithm

Answer

Breadth-First Search (BFS)

Answer

Prim's Algorithm

Question 48

In a weighted graph, what is the purpose of finding a minimum spanning tree?

Accepted Answer

To identify the subgraph that connects all vertices with the lowest total edge weight

Answer

To find the shortest path between two specified vertices

Answer

To find the subgraph with the highest total edge weight

Question 49

Which algorithm is commonly utilized for finding strongly connected components in a directed graph?

Accepted Answer

Kosaraju's Algorithm

Answer

Floyd-Warshall Algorithm

Answer

Dijkstra's Algorithm

Answer

Bellman-Ford Algorithm

Question 50

For a graph with n vertices and m edges, what is the time complexity of checking bipartiteness using BFS traversal?

Accepted Answer

O(V + E)

Answer

O(V^2)

Answer

O(V^3)

Answer

O(E^2)