See attached, answer part 2 **Problem 6****Part 1.** Give the adjacency matrix for the graph G as pictured below:![Graph with 6 vertices and 9 edges](image.png)*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.**Part 2.** A directed graph G has 5 vertices, numbered 1 through 5. The $5 \times 5$ matrix $A$ is the adjacency matrix for G. The matrices $A^2$ and $A^3$ are given below.\[A^2 = \begin{bmatrix}0 & 1 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 1 & 0 \\0 & 1 & 0 & 1 & 0 \end{bmatrix}\]\[A^3 = \begin{bmatrix}1 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 \\1 & 1 & 0 & 1 & 0\end{bmatrix}\]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: $A^4 = A^2 \cdot A^2$)

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Description: See attached, answer part 2 **Problem 6****Part 1.** Give the adjacency matrix for the graph G as pictured below:![Graph with 6 vertices and 9 edges](image.png)*Figure 2:* A graph shows 6 vertices and 9 edges. The vertices are 1, 2, 3, 4, 5, and 6, r

A directed graph G has 5 vertices, numbered 1 through 5. The matrix A is the adjacency matrix for…

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PROBLEM 6 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 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 A? and A are given below. 0 1 0 0 0 O 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 10 1 1 0 0 0 0 O o 1 0 0 O 0 0 0 10 0 0 1 10 1 1 1 0 10 A² = A³ = 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)

PROBLEM 6 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 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 A? and A are given below. 0 1 0 0 0 O 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 10 1 1 0 0 0 0 O o 1 0 0 O 0 0 0 10 0 0 1 10 1 1 1 0 10 A² = A³ = 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)

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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See attached, answer part 2

**Problem 6**

**Part 1.** Give the adjacency matrix for the graph G as pictured below:

![Graph with 6 vertices and 9 edges](image.png)

*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.

**Part 2.** A directed graph G has 5 vertices, numbered 1 through 5. The $5 \times 5$ matrix $A$ is the adjacency matrix for G. The matrices $A^2$ and $A^3$ are given below.

\[
A^2 = \begin{bmatrix}
0 & 1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 \\
1 & 0 & 0 & 1 & 0 \\
0 & 1 & 0 & 1 & 0
\end{bmatrix}
\]

\[
A^3 = \begin{bmatrix}
1 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 \\
1 & 1 & 0 & 1 & 0
\end{bmatrix}
\]

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: $A^4 = A^2 \cdot A^2$)

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