Find the number of connected components for each of the following graphs. (a) A graph with 8 vertices and 6 edges is shown. Vertex a is connected to vertex b and to vertex d. Vertex b is connected to vertex a and to vertex c. Vertex c is connected to vertex b and to vertex d. Vertex d is connected to vertex a and to vertex c. Vertex e is isolated. Vertex f is connected to vertex g. Vertex g is connected to vertex f and to vertex h. Vertex h is connected to vertex g. (b) A graph with 6 vertices and 6 edges is shown. Vertex u is connected to vertex w and to vertex y. Vertex v is connected to vertex x and to vertex z. Vertex w is connected to vertex u and to vertex y. Vertex x is connected to vertex v and to vertex z. Vertex y is connected to vertex u and to vertex w. Vertex z is connected to vertex v and to vertex x. (c) A graph with 10 vertices and 8 edges is shown. Vertex a is connected to vertex b. Vertex b is connected to vertex a and to vertex d. Vertex c is connected to vertex c by a loop and to vertex i. Vertex d is connected to vertex b and to vertex e. Vertex e is connected to vertex d. Vertex f is connected to vertex g. Vertex g is connected to vertex f. Vertex h is connected to vertex i. Vertex i is connected to vertex c, to vertex h, and to vertex j. Vertex j is connected to vertex i. (d) A graph with 4 vertices and 2 edges is shown. Vertex v1 is connected to vertex v3. Vertex v2 is connected to vertex v4. Vertex v3 is connected to vertex v1. Vertex v4 is connected to vertex v2.
Find the number of connected components for each of the following graphs. (a) A graph with 8 vertices and 6 edges is shown. Vertex a is connected to vertex b and to vertex d. Vertex b is connected to vertex a and to vertex c. Vertex c is connected to vertex b and to vertex d. Vertex d is connected to vertex a and to vertex c. Vertex e is isolated. Vertex f is connected to vertex g. Vertex g is connected to vertex f and to vertex h. Vertex h is connected to vertex g. (b) A graph with 6 vertices and 6 edges is shown. Vertex u is connected to vertex w and to vertex y. Vertex v is connected to vertex x and to vertex z. Vertex w is connected to vertex u and to vertex y. Vertex x is connected to vertex v and to vertex z. Vertex y is connected to vertex u and to vertex w. Vertex z is connected to vertex v and to vertex x. (c) A graph with 10 vertices and 8 edges is shown. Vertex a is connected to vertex b. Vertex b is connected to vertex a and to vertex d. Vertex c is connected to vertex c by a loop and to vertex i. Vertex d is connected to vertex b and to vertex e. Vertex e is connected to vertex d. Vertex f is connected to vertex g. Vertex g is connected to vertex f. Vertex h is connected to vertex i. Vertex i is connected to vertex c, to vertex h, and to vertex j. Vertex j is connected to vertex i. (d) A graph with 4 vertices and 2 edges is shown. Vertex v1 is connected to vertex v3. Vertex v2 is connected to vertex v4. Vertex v3 is connected to vertex v1. Vertex v4 is connected to vertex v2.
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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Find the number of connected components for each of the following graphs.
(a)
A graph with 8 vertices and 6 edges is shown.
- Vertex a is connected to vertex b and to vertex d.
- Vertex b is connected to vertex a and to vertex c.
- Vertex c is connected to vertex b and to vertex d.
- Vertex d is connected to vertex a and to vertex c.
- Vertex e is isolated.
- Vertex f is connected to vertex g.
- Vertex g is connected to vertex f and to vertex h.
- Vertex h is connected to vertex g.
(b)
A graph with 6 vertices and 6 edges is shown.
- Vertex u is connected to vertex w and to vertex y.
- Vertex v is connected to vertex x and to vertex z.
- Vertex w is connected to vertex u and to vertex y.
- Vertex x is connected to vertex v and to vertex z.
- Vertex y is connected to vertex u and to vertex w.
- Vertex z is connected to vertex v and to vertex x.
(c)
A graph with 10 vertices and 8 edges is shown.
- Vertex a is connected to vertex b.
- Vertex b is connected to vertex a and to vertex d.
- Vertex c is connected to vertex c by a loop and to vertex i.
- Vertex d is connected to vertex b and to vertex e.
- Vertex e is connected to vertex d.
- Vertex f is connected to vertex g.
- Vertex g is connected to vertex f.
- Vertex h is connected to vertex i.
- Vertex i is connected to vertex c, to vertex h, and to vertex j.
- Vertex j is connected to vertex i.
(d)
A graph with 4 vertices and 2 edges is shown.
- Vertex v1 is connected to vertex v3.
- Vertex v2 is connected to vertex v4.
- Vertex v3 is connected to vertex v1.
- Vertex v4 is connected to vertex v2.
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