Does a simple graph on eight vertices of degrees 1, 1, 2, 2, 3, 3, 4, 4 exist? Either draw such a graph or explain why no such graph exists.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Question 11 Plz provide hand written answer asap
11.
(a) Does a simple graph on eight vertices of degrees 1, 1, 2, 2, 3, 3, 4, 4 exist?
Either draw such a graph or explain why no such graph exists.
(b) Is there a simple connected graph having 9 vertices and 7 edges?
Either draw such a graph or explain why no such graph exists.
(c) Is there a simple graph such that the third power of its adjacency matrix A equals to
[o 2 0 1
A = 2 1 3 0
0 3 2 2
Either draw such a graph or explain why no such graph exists.
10 2 1
Transcribed Image Text:11. (a) Does a simple graph on eight vertices of degrees 1, 1, 2, 2, 3, 3, 4, 4 exist? Either draw such a graph or explain why no such graph exists. (b) Is there a simple connected graph having 9 vertices and 7 edges? Either draw such a graph or explain why no such graph exists. (c) Is there a simple graph such that the third power of its adjacency matrix A equals to [o 2 0 1 A = 2 1 3 0 0 3 2 2 Either draw such a graph or explain why no such graph exists. 10 2 1
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