$Graph theory question on Euler circuit, Euler path, Hamilton circuit, and Hamilton path$

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$Graph theory question on Euler circuit, Euler path, Hamilton circuit, and Hamilton path$

Please answer with all the conditions.

Discrete Mathematics

Sara

13

Matchmaticians Graph theory question on Euler circuit, Euler path, Hamilton circuit, and Hamilton path  File #1

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Naturelover

+1

Low bounty!
- Naturelover
  
  +1
  
  Still very low!
- Sara
  
  0
  
  Can you solve c and d only?
Sara

0

Can you solve d and c only?
- Naturelover
  
  0
  
  Yes, but I think a fair bounty even for half of it is $10. For determining a fair bounty, imagine how much time one would spend to solve your question and multiply by an hourly rate that makes sense.
Naturelover

0

I'll do it for you this time. But remember, this is still a low bounty.

Answer

The answer is accepted.

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Naturelover

+1

Low bounty!

Naturelover

+1

Still very low!

Sara

0

Can you solve c and d only?
Sara

0

Can you solve d and c only?

Naturelover

0

Yes, but I think a fair bounty even for half of it is $10. For determining a fair bounty, imagine how much time one would spend to solve your question and multiply by an hourly rate that makes sense.
Naturelover

0

Yes, but I think a fair bounty even for half of it is $10. For determining a fair bounty, imagine how much time one would spend to solve your question and multiply by an hourly rate that makes sense.
Naturelover

0

I'll do it for you this time. But remember, this is still a low bounty.

Answer 1

Answers can only be viewed under the following conditions:

The questioner was satisfied with and accepted the answer, or
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a. No

Euler Circuit is a circuit that uses every edge in a graph with no repeats (starting and ending at the same vertex). An easier way to find out is that in an Euler Circuit every vertex must have an even degree (equal number of edges going to and leaving those vertices). In this graph, the four corners

Vertices 1, 3, 11, 13 all have an odd degree (3 degrees)

b. No

This graph does not have a Euler Path. An Euler path is a path that uses every edge in a graph with no repeats. Being a path, it does not have to return to the starting vertex. Easier way to find out is using the Euler's Theorem: If a graph has more than 2 vertices of odd degree then it has no Euler paths. As mentioned above, this graph has 4 vertices with odd degrees.

c. Yes

Hamilton Circuit

A Hamilton circuit is a circuit that visits every vertex once with no repeats. This graph consist of a Hamilton circuit as below:

1-4-2-5-3-8-13-10-7-9-12-11-6-1

d. Yes

The Hamilton Path (or traceable path) is as below:

1-4-2-5-3-8-13-10-7-9-12-11-6

Naturelover

88

Sara

0

The dirac’s theorem and ore’s theorem cannot be used right?
- Naturelover
  
  0
  
  No! They won't work.
Sara

0

Ok thank you

$Graph theory question on Euler circuit, Euler path, Hamilton circuit, and Hamilton path$

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