. In each of the following graphs, find paths of length 9 and 11, and cycles of length 5, 6, 8 and 9, if possible. G₁ * G₂
. In each of the following graphs, find paths of length 9 and 11, and cycles of length 5, 6, 8 and 9, if possible. G₁ * G₂
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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Four Math Questions
How can I solve and answer these four math questions showed in the screenshot?
![1. In each of the following graphs, find paths of length 9 and 11, and cycles of length 5, 6, 8
and 9, if possible.
G₁
105
G₁
2. (a) Prove that if G is a graph of minimum degree 3, then G contains a path of length 4.
(b) Prove that if G is a graph of minimum degree 5, then G contains a path of length 5.
3. Find the length of the shortest path for each of the following graphs.
10
G₂
10
G3
4. A tree is a graph containing no circuits. Let T be a tree with 12 vertices that has exactly 3
vertices of degree 3 and exactly one vertex of degree 2.
a. Find the degree sequence of T.
b. Find two different trees with this degree sequence (they need to be more than
visually different but should have a different edge set)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c42be52-d985-41dc-9f5d-8ba980b8b307%2Fb067d485-6597-46e3-b090-c884dc8845a0%2Fe26envm_processed.png&w=3840&q=75)
Transcribed Image Text:1. In each of the following graphs, find paths of length 9 and 11, and cycles of length 5, 6, 8
and 9, if possible.
G₁
105
G₁
2. (a) Prove that if G is a graph of minimum degree 3, then G contains a path of length 4.
(b) Prove that if G is a graph of minimum degree 5, then G contains a path of length 5.
3. Find the length of the shortest path for each of the following graphs.
10
G₂
10
G3
4. A tree is a graph containing no circuits. Let T be a tree with 12 vertices that has exactly 3
vertices of degree 3 and exactly one vertex of degree 2.
a. Find the degree sequence of T.
b. Find two different trees with this degree sequence (they need to be more than
visually different but should have a different edge set)
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