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#51 2012-03-12 12:22:57

bobbym
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Re: Interesting transformations on graphs!!!

Looking at your transformation, is there any rule to determine how it is to be done?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#52 2012-03-12 12:25:06

anonimnystefy
Real Member

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Re: Interesting transformations on graphs!!!

Didn't you read the definition of the transformation in #2?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#53 2012-03-12 12:51:47

anonimnystefy
Real Member

Online

Re: Interesting transformations on graphs!!!

Do you understand the transformation now?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#54 2012-03-12 12:59:42

bobbym
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Re: Interesting transformations on graphs!!!

Not yet. I will need more time to look at it.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#55 2012-03-12 13:00:20

bobbym
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Re: Interesting transformations on graphs!!!

Hi;

I have not even verified the truth that your transformation has the same D number.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#56 2012-03-12 13:07:22

anonimnystefy
Real Member

Online

Re: Interesting transformations on graphs!!!

Do you have doubt in me?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#57 2012-03-12 13:13:17

bobbym
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Re: Interesting transformations on graphs!!!

Not in you but mathematics is a prove it sort of endeavor. Everyone makes mistakes.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#58 2012-03-12 13:17:33

anonimnystefy
Real Member

Online

Re: Interesting transformations on graphs!!!

Hi bobbym

It's easy for to show that making a loop disappear does nothing to the drawability of a graph.

It is also easy to prove the same thing for deleting any cycle.

And it is easy to prove the general statement by showing that it works for any three general nodes.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#59 2012-03-12 13:20:06

bobbym
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Re: Interesting transformations on graphs!!!

First, I like to convince myself of an ideas validity. This can be done empirically.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#60 2012-03-12 13:28:38

anonimnystefy
Real Member

Online

Re: Interesting transformations on graphs!!!

Hi bobbym

Than do that.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#61 2012-03-12 13:36:55

bobbym
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Re: Interesting transformations on graphs!!!

One thing at a time. Is it not very, very late over there?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#62 2012-03-12 13:58:52

anonimnystefy
Real Member

Online

Re: Interesting transformations on graphs!!!

Hi bobbym

Yes, yes it is. tongue

Now convince yourself that what I conjectured is true.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#63 2012-03-12 18:23:45

bobbym
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Re: Interesting transformations on graphs!!!

Hi;

For your example:

http://www.mathisfunforum.com/showimage.php?pid=203914&filename=graf6.JPG

Drawability of the left is 5 and of the right is 6. Drawability property does not hold under the transformation.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#64 2012-03-12 22:24:52

anonimnystefy
Real Member

Online

Re: Interesting transformations on graphs!!!

Hi bobbym

My mistake.First, I didn't draw it correctly, because there should remain only one of those on the right picture, and that's the lefter one.

Second, how did you manage to get the drawability when not all nodes are given?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#65 2012-03-12 22:25:49

bobbym
Administrator

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Re: Interesting transformations on graphs!!!

I have a technique that seems to be working.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#66 2012-03-12 23:07:23

anonimnystefy
Real Member

Online

Re: Interesting transformations on graphs!!!

hi bobbym

i edited #2.

and what technique?

on the pic i posted that shows the definition of the transformation (that's the second picture) those edges that have an open end have nodes on that side but on those nodes that are not shown you might have more nodes with more edges.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#67 2012-03-12 23:08:06

bobbym
Administrator

Offline

Re: Interesting transformations on graphs!!!

I use a pen and paper!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#68 2012-03-12 23:11:41

anonimnystefy
Real Member

Online

Re: Interesting transformations on graphs!!!

hi bobbym

so what?there's still no way to calculate the drawability of the given graphs.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#69 2012-03-12 23:13:05

bobbym
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Re: Interesting transformations on graphs!!!

I disagree. 5  lines do the first one and 6 do the second one.

I am having connection problems so I am just going to shut down and get some rest see you later.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#70 2012-03-12 23:27:03

anonimnystefy
Real Member

Online

Re: Interesting transformations on graphs!!!

hi bobbym

it's 5 on both.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#71 2012-03-13 02:58:51

bobbym
Administrator

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Re: Interesting transformations on graphs!!!

Which both? The old ones or the new ones?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#72 2012-03-13 07:06:26

anonimnystefy
Real Member

Online

Re: Interesting transformations on graphs!!!

Hi bobbym

The drawability is 5 on both sides of the second pic I posted.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#73 2012-03-13 07:10:00

bobbym
Administrator

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Re: Interesting transformations on graphs!!!

Hi;

Agreed, the new picture has 5 on both sides. Now how do we know that always holds?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#74 2012-03-13 07:21:04

anonimnystefy
Real Member

Online

Re: Interesting transformations on graphs!!!

Hi bobbym

Like I said, we could check that out holds for three arbitrary nodes on a graph with k, l and m edges sticking out of those three nodes.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#75 2012-03-13 07:23:10

bobbym
Administrator

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Re: Interesting transformations on graphs!!!

How about more nodes than 3?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

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