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#1 2013-08-15 00:20:58

dee93
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Registered: 2013-08-12
Posts: 19

Which of the following graphs are Eulerian and which are Hamiltonian?

Would I be right in saying that the first and second graphs are Hamiltonian and the third is Eulerian,unsure about the 4th?

View Image: graphs.jpg

Last edited by dee93 (2013-08-15 00:31:10)

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#2 2013-08-15 00:39:03

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,190
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Re: Which of the following graphs are Eulerian and which are Hamiltonian?

fourth is eulerian too


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
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#3 2013-08-15 01:00:26

dee93
Member
Registered: 2013-08-12
Posts: 19

Re: Which of the following graphs are Eulerian and which are Hamiltonian?

Agnishom wrote:

fourth is eulerian too

thanks so i am correct with the others?

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#4 2013-08-15 01:06:00

bob bundy
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Registered: 2010-06-20
Posts: 6,471

Re: Which of the following graphs are Eulerian and which are Hamiltonian?

I'm looking now.  First is H but not E

More ....

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#5 2013-08-15 01:16:34

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,471

Re: Which of the following graphs are Eulerian and which are Hamiltonian?

Note:   It is possible to be both          eg.  Four vertices connected as a square.

Second is not H and is E

Don't see how this is H?  The middle vertex must be visited twice and three times if it is the start/finish.

Third is H but not E

Fourth is   not H and is E

Bob

http://www-groups.mcs.st-andrews.ac.uk/ … tonian.pdf


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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