PROBLEM 6 Part 1. Give the adjacency matrix for the graph G as pictured below: 2 3 Figure 2: A graph shows 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 arrows, 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 vertex 5.
PROBLEM 6 Part 1. Give the adjacency matrix for the graph G as pictured below: 2 3 Figure 2: A graph shows 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 arrows, 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 vertex 5.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:PROBLEM 6
Part 1. Give the adjacency matrix for the graph G as pictured below:
(2
3
6
Figure 2: A graph shows 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 arrows,
as follows: 4 to 3; 3 to 2; 2 to 1; I to 6; 6 to 2; 3 to 4; 4 to 5; 5 to 6; and a self loop on
vertex 5.
Part 2. A directed graph G has 5 vertices, numbered 1 through 5. The 5 × 5
matrix A is the adjacency matrix for G. The matrices A² and A³ are given below.
0 1 0 0 0
O 0 0 10 0 0
1 0 0 0 0
1 0 0 1 0
1 1 0
A² =
1.
1 0 0 0 0
1 0 0 0 0
0 0 10 0
0 1 10 1
1 0 1 0
A3 =
1
Use the information given to answer the questions about the graph
(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: A4=
A? A?.)
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