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Math Help - k-regular graphs

  1. #1
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    k-regular graphs

    I have a question which says "for every even integer n > 2 construct a connected 3-regular graph with n vertices".

    I know what a 3-regular graph is and how to draw one etc etc...

    But am i meant to construct graph for every even integer n > 2??

    Can somebody tell me if this question means something else? I may be missing the idea here...cheers people!
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  2. #2
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    Quote Originally Posted by pupnat View Post
    I have a question which says "for every even integer n > 2 construct a connected 3-regular graph with n vertices".

    I know what a 3-regular graph is and how to draw one etc etc...

    But am i meant to construct graph for every even integer n > 2??

    Can somebody tell me if this question means something else? I may be missing the idea here...cheers people!
    they want you to, for any even integer n, construct a 3-regular graph with n verices. here's one way to do it: label the vertices as 1,2, \cdots , 2m=n, and choose the edges to be:

    (1,2), (2,3), (3,4), \cdots , (2m-1,2m), (2m,1) and (2,2m), (3,2m-1), (4,2m-2),\cdots , (m+1,1).
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