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Discrete Mathematics I need help with this 2 part problem Part a Part b

Discrete Mathematics I need help with this 2 part problem Part a Part b

Advanced Engineering Mathematics
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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Discrete Mathematics I need help with this 2 part problem Part a Part b
ignment.tex - TeXstudio part label tiny 8 of 16 3 7. (ii) Figure 8: An undirected graph has 8 vertices, 1 through 8. 4 ver- tices form a rectangular shape in the center. Starting from the top left verter and moving clockwise, the vertices of the rectangular shape are, 3. 7. 5. and 6. Verter 2 is at about the center of the rectangular shape. Verter 8 is to the right of the rectangular shape. Verter 1 and 4 are to the left of the rectangular shape, horizontally in-line with vertices 3 and 6. respectively. Undirected edges, line segments, are between the following vertices: 1 and 3; 3 and 7; 3 and 4: 3 and 6: 3 and 2: 4 and 2: 4 and 6: 6 and 2; 6 and 5; 2 and 5; 2 and 7; 2 and 8; 7 and 5: 7 and 8: and 5 and 8.
Transcribed Image Text:ignment.tex - TeXstudio part label tiny 8 of 16 3 7. (ii) Figure 8: An undirected graph has 8 vertices, 1 through 8. 4 ver- tices form a rectangular shape in the center. Starting from the top left verter and moving clockwise, the vertices of the rectangular shape are, 3. 7. 5. and 6. Verter 2 is at about the center of the rectangular shape. Verter 8 is to the right of the rectangular shape. Verter 1 and 4 are to the left of the rectangular shape, horizontally in-line with vertices 3 and 6. respectively. Undirected edges, line segments, are between the following vertices: 1 and 3; 3 and 7; 3 and 4: 3 and 6: 3 and 2: 4 and 2: 4 and 6: 6 and 2; 6 and 5; 2 and 5; 2 and 7; 2 and 8; 7 and 5: 7 and 8: and 5 and 8.
assignment.tex - TeXstudio part label tiny 7 of 16 (a) Find the connected components of each graph. (i) G = (V, E). V = {a, b, c, d, e}. E =0 (ii) G = (V, E). V= {a, b, c, d, e, f). E = {{c, f}, {a, b}, {d, a}, {e, c}, {b, S}} (b) Determine the edge connectivity and the vertex connectivity of each graph. 3 Figure 7: An undirected graph has 8 vertices, 1 through 8. 4 ver- tices form a rectangular-shape on the left. Starting from the top left verter and moving clockwise, the vertices of the rectangular shape are, 1, 2, 3, and 4. 3 vertices form a triangle on the right, with a vertical side on the left and the other verter on the extreme right. Starting from the top verter and moving clockuise, the vertices of the triangu- lar shape are, 7, 8, and 5. Verter 6 is between the rectangular shape and the triangular shape. Undirected edges, line segments, are between the following vertices: 1 and 2; 2 and 3; 3 and 4: 4 and 1: 2 and 6; 4 and 6: 3 and 6: 6 and 7; 6 and 8; 6 and 5: 7 and 5: 7 and 8; and 5 and 8. Rager 7 to 8 of 16 108%
Transcribed Image Text:assignment.tex - TeXstudio part label tiny 7 of 16 (a) Find the connected components of each graph. (i) G = (V, E). V = {a, b, c, d, e}. E =0 (ii) G = (V, E). V= {a, b, c, d, e, f). E = {{c, f}, {a, b}, {d, a}, {e, c}, {b, S}} (b) Determine the edge connectivity and the vertex connectivity of each graph. 3 Figure 7: An undirected graph has 8 vertices, 1 through 8. 4 ver- tices form a rectangular-shape on the left. Starting from the top left verter and moving clockwise, the vertices of the rectangular shape are, 1, 2, 3, and 4. 3 vertices form a triangle on the right, with a vertical side on the left and the other verter on the extreme right. Starting from the top verter and moving clockuise, the vertices of the triangu- lar shape are, 7, 8, and 5. Verter 6 is between the rectangular shape and the triangular shape. Undirected edges, line segments, are between the following vertices: 1 and 2; 2 and 3; 3 and 4: 4 and 1: 2 and 6; 4 and 6: 3 and 6: 6 and 7; 6 and 8; 6 and 5: 7 and 5: 7 and 8; and 5 and 8. Rager 7 to 8 of 16 108%
Expert Solution
Step 1

To find- 

  1. Find the connected components of each graph.
  1. G = V, E,   V = a, b, c, d, e,    E = ϕ
  2. G = V, E,   V = a, b, c, d, e, f,    E = c, f, a, b, d, a, e, c, b, f

    b. Determine the edge connectivity and the vertex connectivity of each graph.

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