Im having difficulties with part 2 of this page. I'm not sure if the graph from the top half is used in the part 2 so I'm including it. Also please type your answer, I've had issues reading handwriting before. Thank you. **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: 1 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 matrix A is the adjacency matrix for G. The matrices \( A^2 \) and \( A^3 \) are given below.\[A = \begin{bmatrix}0 & 1 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 1 \\1 & 0 & 1 & 0 & 1 \end{bmatrix}\]\[A^3 =\begin{bmatrix}1 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 1 \\2 & 0 & 1 & 0 & 2 \\1 & 0 & 1 & 0 & 1 \\2 & 0 & 1 & 0 & 2 \end{bmatrix}\]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: \( A^4 = A^3 \times A \)).This exercise helps students understand the relationship between a graph's adjacency matrix and walks of certain lengths within the graph. The matrices \( A^2 \) and \( A^3 \) show the paths of lengths 2 and 3, respectively.

Step:-1 The given figure in part ! is not used part 2 because it has 6 vertices and in part 2…

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 A? and A3 are given below. 1 0 0 10 00 ***00 42 00 0 0I ***I 10 1 0. %3D 10 0 0 I 00 0 10 Use the information given to answer the questions about the graph G. 3. (a) Which vertices can reach vertex 2 by a walk of length 3? 0110 1 10 **0 0 (b) Is there a walk of length 4 from vertex 4 to vertex 5 in G? (Hint: A = A?. A2.)

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 A? and A3 are given below. 1 0 0 10 00 00 42 00 0 0I I 10 1 0. %3D 10 0 0 I 00 0 10 Use the information given to answer the questions about the graph G. 3. (a) Which vertices can reach vertex 2 by a walk of length 3? 0110 1 10 **0 0 (b) Is there a walk of length 4 from vertex 4 to vertex 5 in G? (Hint: A = A?. 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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