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Thread: Isomorphism

  1. #1 Isomorphism 
    Forum Ph.D. Heinsbergrelatz's Avatar
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    What does one mean when they ask, determine if the two graphs below are isomorphic.

    what is isomorphism? i just interacted with a new branch of mathematics known as graph theory. just when i though i could take a break, graph theory now haunts me.

    any good internet links,books, tips?

    thank you


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    "Mathematicians stand on each other's shoulders."- Carl Friedrich Gauss


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  3. #2  
    Forum Ph.D. Leszek Luchowski's Avatar
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    This Wikipedia entry:

    http://en.wikipedia.org/wiki/Isomorphism

    contains these explicit words:

    In graph theory, an isomorphism between two graphs G and H is a bijective map f from the vertices of G to the .....
    Have a look at that definition, and, if you need, the definition of "bijective" which is linked to that word. If you find something that's not clear to you, I'm sure a lot of people around here will help you decipher it.


    Leszek. Pronounced [LEH-sheck]. The wondering Slav.
    History teaches us that we don't learn from history.
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  4. #3  
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    They might, but it won't be me! I answered this question once before, and the poster admitted he hadn't even read my response.

    Who was this poster? Our current one! so I shan't waste my time again. Let him refer back to this thread and THINK why a bijective function defines an isomorphism. It's all there, and it is a quite general construction i.e. not only in graph theory
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  5. #4  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    They might, but it won't be me! I answered this question once before, and the poster admitted he hadn't even read my response.

    Who was this poster? Our current one! so I shan't waste my time again.
    why did you even bother to respond?
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  6. #5  
    Forum Ph.D. Leszek Luchowski's Avatar
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    Quote Originally Posted by Heinsbergrelatz
    why did you even bother to respond?
    Apparently, he wanted to save my time, and that of other people.

    Heinsberg, it is a common problem with young netters that they feel as if they are just communicating with a computer system. For example - they get an answer that's difficult for them to understand, so they just ignore it, without so much as a "thank you" or "please explain what you mean by...", reset the system (or imagine that they did) and run the same question through it again. This may or may not be your case; I'll leave that for you to figure out.

    I have had a look at that previous thread and it seems you were overwhelmed by abstract mathematical terms that sounded unfamiliar and cryptic to you (they do to many people). You should have simply said so.

    I am still willing to help you - tell me what you don't understand in the Wikipedia articles I linked. And also tell me what you do understand there, so we can start from that, however little it might be.
    Leszek. Pronounced [LEH-sheck]. The wondering Slav.
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  7. #6  
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    Quote Originally Posted by Heinsbergrelatz

    why did you even bother to respond?
    Actually, I wasn't responding to you, I was responding to Leszek. True, my response WAS about you, and if that caused offence, I am sorry.

    Let's establish a rule, between friends. OK?

    I ask a question. I get an answer (that I have read) which I don't understand. I ask another question. I get another answer and again I ask a question and again get an answer and so on....

    I call this a constructive discussion between members who have similar interests, but possibly different levels of expertise.

    That's GREAT! The questioner has learned something! Isn't that what internet fora are supposed to be about?
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  8. #7 Re: Isomorphism 
    . DrRocket's Avatar
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    Quote Originally Posted by Heinsbergrelatz
    What does one mean when they ask, determine if the two graphs below are isomorphic.

    what is isomorphism? i just interacted with a new branch of mathematics known as graph theory. just when i though i could take a break, graph theory now haunts me.

    any good internet links,books, tips?

    thank you

    Basically, in mathematics two objects are isomorphic if to all intents and purposes they are the same thing.

    In algebra an isomorphism is a bijective function that preserves all algebraic operations of interest. In topology an isomorphism is a homeomorphism. Two smooth manifolds are isomorphic if they are diffeomorphic.

    One can make this precise using category theory, but it is a bit pedantic.
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