(b) Determine the edge connectivity and the vertex connectivity of each graph. 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 vertex and moving clockwise, 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. 2 5. (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. Vertex 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.
(b) Determine the edge connectivity and the vertex connectivity of each graph. 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 vertex and moving clockwise, 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. 2 5. (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. Vertex 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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question
Please answer part b (i) and (ii)
Transcribed Image Text:(b) Determine the edge connectivity and the vertex connectivity of each graph.
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 vertex and moving clockwise, 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.
2
5.
(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. Vertex 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.
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