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: \( A^4 = A^2 \cdot A^2 \)).

Name: part 1 and 2 **Problem 6****Part 1.** Give the adjacency matrix for th
Uploaded: 2024-03-20T06:46:03.000Z
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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