part 1 and 2 **Problem 6****Part 1.** Give the adjacency matrix for the graph $ G $ as pictured below:*Image Description:*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.\[A^2 =\begin{bmatrix}0 & 1 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 & 0 \\0 & 1 & 1 & 0 & 0 \\0 & 1 & 1 & 1 & 0 \\\end{bmatrix}\]\[A^3 =\begin{bmatrix}0 & 0 & 1 & 0 & 0 \\0 & 1 & 0 & 0 & 0 \\0 & 0 & 1 & 1 & 0 \\0 & 1 & 0 & 1 & 0 \\1 & 1 & 0 & 1 & 0 \\\end{bmatrix}\]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: part 1 and 2 **Problem 6****Part 1.** Give the adjacency matrix for the graph $ G $ as pictured below:*Image Description:*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 ver

Part -1: Given the graph, We know that, aij=1 if there is path between the vertices aij=0…

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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.)

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.)

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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part 1 and 2

**Problem 6**

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

*Image Description:*
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.

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

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

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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