(a) Find the connected components of cach graph.(1) G = (V, E). V= {a, b, c, d, e}. E= @(ii) G = (V, E). V = {a, b, c, d, e, ƒ}. E= {{c, S}, {a, b}, {d, a}, {e, c}, {b, S}}(b) Determine the edge connectivity and the vertex connectivity of cach 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 leftvertez 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 verticalside on the left and the other verter on the extreme right. Startingfrom the top vertez and moving clockwise, the vertices of the triangu-lar shape are, 7, 8, and 5. Vertez 6 is between the rectangular shapeand the triangular shape. Undirected edges, line segments, are betweenthe following vertices: 1 and 2; 2 and 3; 3 and 4; 4 and 1; 2 and 6; 4and 6; 3 and 6; 6 and 7; 6 and 8; 6 and 5; 7 and 5; 7 and 8; and 5and 8. 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 leftvertez and moving clockwise, the vertices of the rectangular shape are,3, 7, 5, and 6. Vertez 2 is at about the center of the rectangular shape.Vertez 8 is to the right of the rectangular shape. Vertez 1 and 4 areto the left of the rectangular shape, horizontally in-line with vertices 3and 6, respectively. Undirected edges, line segments, are between thefollowing vertices: 1 and 3; 3 and 7; 3 and 4; 3 and 6; 3 and 2; 4 and2; 4 and 6; 6 and 2; 6 and 5; 2 and 5; 2 and 7; 2 and 8; 7 and 5; 7and8;and 5 and 8.

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Description: (a) Find the connected components of cach graph.(1) G = (V, E). V= {a, b, c, d, e}. E= @(ii) G = (V, E). V = {a, b, c, d, e, ƒ}. E= {{c, S}, {a, b}, {d, a}, {e, c}, {b, S}}(b) Determine the edge connectivity and the vertex connectivity of cach graph

Answer for sub question a: Given graph is, G=V,E,V=a,b,c,d,e, E=∅ 1) Note: A vertex with no…

Answered: 5 (i) | bartleby

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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(a) Find the connected components of cach graph.
(1) G = (V, E). V= {a, b, c, d, e}. E= @
(ii) G = (V, E). V = {a, b, c, d, e, ƒ}. E= {{c, S}, {a, b}, {d, a}, {e, c}, {b, S}}
(b) Determine the edge connectivity and the vertex connectivity of cach 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
vertez 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 vertez and moving clockwise, the vertices of the triangu-
lar shape are, 7, 8, and 5. Vertez 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.

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
vertez and moving clockwise, the vertices of the rectangular shape are,
3, 7, 5, and 6. Vertez 2 is at about the center of the rectangular shape.
Vertez 8 is to the right of the rectangular shape. Vertez 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.

Expert Solution

Step 1

Answer for sub question a:

Given graph is, $G = \{V, E\}, V = \{a, b, c, d, e\}, E = \emptyset$

1) Note: A vertex with no incident edges is itself a component.

Since the given graph has no edges, no edges are incident on any of the vertices.

Therefore, each vertex is a component.

Therefore, number of components in the given graph is $5$ .

Step 2

2) The given graph is

$G = \{V, E\}, V = \{a, b, c, d, e, f\}, E = \{\{e, f\} \{a, b\}, \{d, a\}, \{e, c\}, \{b, f\}\}$

First draw the graph.

The given graph is connected and hence it has exactly one component.

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