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[1) representation and the adjacency list representation of the graph. For the following directed graph, provide the adjacency matrix

[1) representation and the adjacency list representation of the graph. For the following directed graph, provide the adjacency matrix

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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**Transcription for Educational Website: Directed Graph Representations** **Problem Statement:** (1) For the following directed graph, provide the adjacency matrix representation and the adjacency list representation of the graph. **Graph Description:** The graph consists of four vertices: A, B, C, and D. The directed edges between these vertices are as follows: - An edge from A to B - An edge from B to C - An edge from C to D - An edge from D to A - An edge from D to B **Adjacency Matrix Representation:** The adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. ``` A B C D A [ 0 1 0 0 ] B [ 0 0 1 0 ] C [ 0 0 0 1 ] D [ 1 1 0 0 ] ``` - Each row represents a source vertex. - Each column represents a destination vertex. - A '1' means there is a directed edge from the source vertex to the destination vertex. A '0' means there is no edge. **Adjacency List Representation:** The adjacency list represents the graph as a collection of unordered lists used to show which vertices are adjacent to which other vertices. - A: [B] - B: [C] - C: [D] - D: [A, B] - Each entry lists a vertex and the vertices to which it has direct outgoing edges. This representation is efficient in terms of space and is particularly useful for sparse graphs.
Transcribed Image Text:**Transcription for Educational Website: Directed Graph Representations** **Problem Statement:** (1) For the following directed graph, provide the adjacency matrix representation and the adjacency list representation of the graph. **Graph Description:** The graph consists of four vertices: A, B, C, and D. The directed edges between these vertices are as follows: - An edge from A to B - An edge from B to C - An edge from C to D - An edge from D to A - An edge from D to B **Adjacency Matrix Representation:** The adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. ``` A B C D A [ 0 1 0 0 ] B [ 0 0 1 0 ] C [ 0 0 0 1 ] D [ 1 1 0 0 ] ``` - Each row represents a source vertex. - Each column represents a destination vertex. - A '1' means there is a directed edge from the source vertex to the destination vertex. A '0' means there is no edge. **Adjacency List Representation:** The adjacency list represents the graph as a collection of unordered lists used to show which vertices are adjacent to which other vertices. - A: [B] - B: [C] - C: [D] - D: [A, B] - Each entry lists a vertex and the vertices to which it has direct outgoing edges. This representation is efficient in terms of space and is particularly useful for sparse graphs.
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Step 1

Adjacency list :-  In this array of list is used. size of array  is equal to the number of vertices . let array be an array[]. array[i] represents the list of vertices adjacent to the ith vertex. 

 

 

Adjacency matrix :  this matrix is in the form of 2D array of size V X V where V is a vertices of a graph .

here we represent 1 if there is edge between two vertices 

and we represent 0 if there is no edge between two vertices

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