Part 1. Give the adjacency matrix for the graph G as pictured below: Figure 2: A graph shows 6 vertices and 9 edges. The vertices are 1, 2, 3, 4, 5, and 6, represented by circles. The cdges between the vertices are represented by arrous, as follows: 4 to 3; 3 to 2; 2 to i; 1 to 6; 6 to 2; 3 to 4; 4 to 5; 5 to 6; and a self loop on vertez 5. Part 2. A directed graph G has 5 vertices, numbered 1 through 5. The 5 x 5 matrix A is the adjacency matrix for G. The matrices A² and Aº are given below. '0 1 0 0 0 0 0 100 10 0 00 1001 0 01101 0 0 00 0 10 0 0 0 0 10 0 0 1 1 0 1 1 1 0 1 0 Use the information given to answer the questions about the graph G. (n) Which vertices can reach vertex 2 by a walk of length 3? (b) Is there a walk of length 4 from vertex 4 to vertex 5 in G? (Hint: A A² · A².)

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 72EQ
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part 1 and 2

PROBLEM 6
Part 1. Give the adjacency matrix for the graph G as pictured below:
(6
Figure 2: A graph shous 6 vertices and 9 edges. The vertices are 1, 2, 3, 4,
5, and 6, represented by circles. The edges between the vertices are represented by
arrous, as follows: 4 to 3; 3 to 2; 2 to 1; 1 to 6; 6 to 2; 3 to 4; 4 to 5; 5 to 6; and
a self loop on verter 5.
Part 2. A directed graph G has 5 vertices, numbered 1 through 5. The 5 x 5
matrix A is the adjacency matrix for G. The matrices A² and A are given below.
0 10 0 0
0 0 10 0
A² =
1
00
00
0 0 1 0
1 1
0 1
1
1 0
0 10 0 0
0 0 10 0
0 1 1 0 1
1 10 1 0
0 0 0
A =
Use the information given to answer the questions about the graph G.
(a) Which vertices can reach vertex 2 by a walk of length 3?
(b) Is there a walk of length 4 from vertex 4 to vertex 5 in G? (Hint: A
A² - A².)
Transcribed Image Text:PROBLEM 6 Part 1. Give the adjacency matrix for the graph G as pictured below: (6 Figure 2: A graph shous 6 vertices and 9 edges. The vertices are 1, 2, 3, 4, 5, and 6, represented by circles. The edges between the vertices are represented by arrous, as follows: 4 to 3; 3 to 2; 2 to 1; 1 to 6; 6 to 2; 3 to 4; 4 to 5; 5 to 6; and a self loop on verter 5. Part 2. A directed graph G has 5 vertices, numbered 1 through 5. The 5 x 5 matrix A is the adjacency matrix for G. The matrices A² and A are given below. 0 10 0 0 0 0 10 0 A² = 1 00 00 0 0 1 0 1 1 0 1 1 1 0 0 10 0 0 0 0 10 0 0 1 1 0 1 1 10 1 0 0 0 0 A = Use the information given to answer the questions about the graph G. (a) Which vertices can reach vertex 2 by a walk of length 3? (b) Is there a walk of length 4 from vertex 4 to vertex 5 in G? (Hint: A A² - A².)
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