Understanding Graph Theory : Torus embedded Hypercube

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I'm trying to understand the graph theory in particularly hypercubes graphs and torus graph.



I have this idea of a torus embedded hypercube but i don't understand it i will be grateful if anyone could help understand how can we embed a torus with a hypercube?
what is the mathematical proof of a torus embedded hypercube?
is it right that we need hypercubes with 4 dimensions
(n = 4 ) to make a torus? or any dimension will be okay?
what is the longest path of a torus embedded hypercube?
what is the Euler tour and the hamiltonian cycle for a torus embedded hypercube?
can we apply this topology on objects in real world? Like connecting things in a shape of a torus embedded hypercube?



I want to to understand the concept of a torus embedded hypercube because I want to apply it in Networks in a project of mine. Any help is welcomed and i'll be grateful if someone could answer my questions and sorry for asking so many.



Thank you all in advance and please forgive my bad english and my ignorance in this field.




graph-theory




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    up vote
    1
    down vote

    favorite












    I'm trying to understand the graph theory in particularly hypercubes graphs and torus graph.



    I have this idea of a torus embedded hypercube but i don't understand it i will be grateful if anyone could help understand how can we embed a torus with a hypercube?
    what is the mathematical proof of a torus embedded hypercube?
    is it right that we need hypercubes with 4 dimensions
    (n = 4 ) to make a torus? or any dimension will be okay?
    what is the longest path of a torus embedded hypercube?
    what is the Euler tour and the hamiltonian cycle for a torus embedded hypercube?
    can we apply this topology on objects in real world? Like connecting things in a shape of a torus embedded hypercube?



    I want to to understand the concept of a torus embedded hypercube because I want to apply it in Networks in a project of mine. Any help is welcomed and i'll be grateful if someone could answer my questions and sorry for asking so many.



    Thank you all in advance and please forgive my bad english and my ignorance in this field.




    graph-theory




    share|cite|improve this question





















      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      I'm trying to understand the graph theory in particularly hypercubes graphs and torus graph.



      I have this idea of a torus embedded hypercube but i don't understand it i will be grateful if anyone could help understand how can we embed a torus with a hypercube?
      what is the mathematical proof of a torus embedded hypercube?
      is it right that we need hypercubes with 4 dimensions
      (n = 4 ) to make a torus? or any dimension will be okay?
      what is the longest path of a torus embedded hypercube?
      what is the Euler tour and the hamiltonian cycle for a torus embedded hypercube?
      can we apply this topology on objects in real world? Like connecting things in a shape of a torus embedded hypercube?



      I want to to understand the concept of a torus embedded hypercube because I want to apply it in Networks in a project of mine. Any help is welcomed and i'll be grateful if someone could answer my questions and sorry for asking so many.



      Thank you all in advance and please forgive my bad english and my ignorance in this field.




      graph-theory




      share|cite|improve this question











      I'm trying to understand the graph theory in particularly hypercubes graphs and torus graph.



      I have this idea of a torus embedded hypercube but i don't understand it i will be grateful if anyone could help understand how can we embed a torus with a hypercube?
      what is the mathematical proof of a torus embedded hypercube?
      is it right that we need hypercubes with 4 dimensions
      (n = 4 ) to make a torus? or any dimension will be okay?
      what is the longest path of a torus embedded hypercube?
      what is the Euler tour and the hamiltonian cycle for a torus embedded hypercube?
      can we apply this topology on objects in real world? Like connecting things in a shape of a torus embedded hypercube?



      I want to to understand the concept of a torus embedded hypercube because I want to apply it in Networks in a project of mine. Any help is welcomed and i'll be grateful if someone could answer my questions and sorry for asking so many.



      Thank you all in advance and please forgive my bad english and my ignorance in this field.





      graph-theory





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      share|cite|improve this question




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      asked Aug 5 at 23:07









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