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; 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 A° are given below. '0 1 0 0 0 00 1 00 00 00 100 1. 0 1 10 0 0 0 0 1 0 0 0 0 0 10 0 0 1 10 1 1 1 0 1 0 A 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 =

Question
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; 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 A° are given below.
'0 1 0 0 0
00
1
00
00
00
100
1.
0 1
10 0 0 0
0 1 0 0 0
0 0 10 0
0 1 10 1
1 1 0 1 0
A
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 =
Expand
Transcribed Image Text

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; 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 A° are given below. '0 1 0 0 0 00 1 00 00 00 100 1. 0 1 10 0 0 0 0 1 0 0 0 0 0 10 0 0 1 10 1 1 1 0 1 0 A 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 =

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